A355924 - OEIS

A355924

Square array A(n,k) = A342671(A246278(n,k)), read by falling antidiagonals, where A342671(x) = gcd(sigma(x), A003961(x)).

3, 1, 1, 3, 1, 1, 3, 1, 1, 1, 3, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 7, 1, 1, 17, 1, 1, 1, 21, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 15, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 19, 1, 1, 1, 1, 1, 37, 1, 1, 1

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

OFFSET

1,1

LINKS

Table of n, a(n) for n=1..105.

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

FORMULA

A(n,k) = A342671(A246278(n,k)).

A(n, k) = gcd(A246278(1+n,k), A355927(n, k)).

EXAMPLE

The top left corner of the array:

n= 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

2n= 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42

-----+-----------------------------------------------------------------------

1 | 3, 1, 3, 3, 3, 1, 3, 1, 3, 21, 3, 15, 3, 1, 3, 9, 3, 1, 3, 9, 3,

2 | 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 5, 1, 13, 1, 1, 5, 1, 1, 5, 1,

3 | 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 7, 1, 7, 1, 1, 1, 13, 7,

4 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 19, 1, 1, 1, 1, 1, 1, 1,

5 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 19, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,

6 | 1, 1, 1, 17, 1, 1, 1, 1, 1, 1, 1, 17, 1, 1, 1, 1, 1, 1, 1, 17, 1,

7 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 19, 1, 1, 1, 1, 1, 1, 29, 1,

8 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,

9 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,

10 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,

11 | 1, 1, 1, 37, 1, 1, 1, 1, 1, 1, 1, 37, 1, 1, 1, 1, 1, 1, 1, 37, 1,

12 | 1, 1, 1, 1, 1, 1, 1, 41, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,

13 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,

14 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,

15 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 61, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,

16 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,

17 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,

18 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,

19 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,

20 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,

21 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,

PROG

(PARI)

up_to = 105;

A246278sq(row, col) = if(1==row, 2*col, my(f = factor(2*col)); for(i=1, #f~, f[i, 1] = prime(primepi(f[i, 1])+(row-1))); factorback(f));

A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };

A342671(n) = gcd(sigma(n), A003961(n));

A355924sq(row, col) = A342671(A246278sq(row, col));

A355924list(up_to) = { my(v = vector(up_to), i=0); for(a=1, oo, for(col=1, a, i++; if(i > up_to, return(v)); v[i] = A355924sq(col, (a-(col-1))))); (v); };

v355924 = A355924list(up_to);

A355924(n) = v355924[n];

CROSSREFS

Cf. A000203, A003961, A246278, A342671, A355833.

Cf. also A355925, A355926, A355927 for similarly constructed arrays.

Sequence in context: A098094 A367824 A087283 * A111625 A109007 A132951

Adjacent sequences: A355921 A355922 A355923 * A355925 A355926 A355927

KEYWORD

nonn,tabl

AUTHOR

Antti Karttunen, Jul 21 2022

STATUS

approved