A085271 -id:A085271

Search: a085271 -id:a085271

Displaying 1-4 of 4 results found.

page 1

A085273

Difference between n-th composite number and its largest prime divisor.

+10
3

2, 3, 6, 6, 5, 9, 7, 10, 14, 15, 15, 14, 11, 21, 20, 13, 24, 21, 25, 30, 22, 17, 28, 33, 19, 26, 35, 35, 33, 40, 23, 45, 42, 45, 34, 39, 51, 44, 49, 38, 29, 55, 31, 56, 62, 52, 55, 51, 46, 63, 69, 37, 70, 57, 66, 65, 75, 78, 41, 77, 68, 43, 58, 77, 85, 78, 69, 62, 47, 76, 93, 91

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Ivan Neretin, Table of n, a(n) for n = 1..10000

EXAMPLE

For 91=7*13 we have 91-13 = 78.

For 92=2*2*23 we have 92-23 = 69.

MATHEMATICA

DeleteCases[Table[n - FactorInteger[n][[-1, 1]], {n, 100}], 0 _] (* Ivan Neretin, Jun 20 2019 *)

PROG

(PARI) cminusp2(n) = { for(x=2, n, forstep(p=x, 2, -1, if(isprime(p) & x%p==0 & isprime(x)==0, print1(x-p, ", "); break); ) ) }

CROSSREFS

Cf. A002808, A085271.

KEYWORD

easy,nonn

AUTHOR

Cino Hilliard, Aug 12 2003

EXTENSIONS

Offset corrected by Ivan Neretin, Jun 20 2019

STATUS

approved

A091114

Number of partitions of n-th composite number containing the smallest prime factor: a(n) = A027293(A002808(n), A056608(n)).

+10
2

2, 5, 11, 11, 22, 42, 77, 77, 135, 231, 385, 385, 627, 1002, 627, 1575, 1575, 2436, 3718, 5604, 5604, 8349, 5604, 12310, 17977, 17977, 26015, 37338, 53174, 53174, 75175, 105558, 53174, 147273, 147273, 204226, 281589, 204226, 386155, 386155

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

a(n) = A000041(A002808(n)) - A091094(n).

a(n) = A000041(A085271(n)). - Charlie Neder, Jan 10 2019

LINKS

Table of n, a(n) for n=1..40.

EXAMPLE

n=2: A002808(2)=6=2*3 has A000041(6)=11 partitions: 6 = 5+1 = 4+2 = 4+1+1 = 3+3 = 3+2+1 = 3+1+1+1 = 2+2+2 = 2+2+1+1 = 2+1+1+1+1 = 1+1+1+1+1+1, 2 occurs in 5 partitions, therefore a(2)=5.

PROG

(PARI) lista(nn) = forcomposite(n=2, nn, print1(numbpart(n - divisors(n)[2]), ", ")); \\ Michel Marcus, Jan 11 2019

CROSSREFS

Cf. A002808, A000041, A020639, A027293, A056608, A085271, A091109, A091094.

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Feb 22 2004

STATUS

approved

A091094

Number of partitions of n-th composite number not containing the smallest prime factor.

+10
1

3, 6, 11, 19, 20, 35, 58, 99, 96, 154, 242, 407, 375, 573, 1331, 861, 1435, 1282, 1886, 2745, 4539, 3961, 9279, 5667, 8038, 13208, 11323, 15836, 22001, 35960, 30383, 41715, 120351, 56953, 92670, 77363, 104566, 247050, 140668, 227999, 188397

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

a(n) = A000041(A002808(n)) - A091114(n).

a(n) = A000041(A002808(n)) - A000041(A085271(n)). - Charlie Neder, Jan 11 2019

LINKS

Table of n, a(n) for n=1..41.

CROSSREFS

Cf. A002808, A000041, A020639, A056608.

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Feb 22 2004

EXTENSIONS

Incorrect formula removed by Charlie Neder, Jan 11 2019

STATUS

approved

A085275

Sum of n-th composite number and its largest prime divisor.

+10
0

6, 9, 10, 12, 15, 15, 21, 20, 18, 21, 25, 28, 33, 27, 30, 39, 30, 35, 35, 34, 44, 51, 42, 39, 57, 52, 45, 49, 55, 50, 69, 51, 56, 55, 68, 65, 57, 66, 63, 76, 87, 65, 93, 70, 66, 78, 77, 85, 92, 77, 75, 111, 80, 95, 88, 91, 85, 84, 123, 91, 102, 129, 116, 99, 95, 104, 115, 124

(list; graph; refs; listen; history; text; internal format)

OFFSET

4,1

LINKS

Table of n, a(n) for n=4..71.

EXAMPLE

For 91=7*13 we have 91+13 = 104; for 92=2*2*23 we have 92+23 = 115.

PROG

(PARI) cminusp3(n) = { for(x=2, n, forstep(p=x, 2, -1, if(isprime(p) & x%p==0 & isprime(x)==0, print1(x+p, ", "); break); ) ) }

CROSSREFS

Cf. A085271, A085273.

KEYWORD

easy,nonn

AUTHOR

Cino Hilliard, Aug 12 2003

STATUS

approved

page 1

Search completed in 0.006 seconds