A300248 - OEIS

A300248

Filter sequence combining A046523(n) and A078898(n), the prime signature of n and the number of times the smallest prime factor of n is the smallest prime factor for numbers <= n.

1, 2, 2, 3, 2, 4, 2, 5, 3, 6, 2, 7, 2, 8, 4, 9, 2, 10, 2, 11, 12, 13, 2, 14, 3, 15, 16, 17, 2, 18, 2, 19, 20, 21, 4, 22, 2, 23, 8, 24, 2, 25, 2, 26, 27, 28, 2, 29, 3, 30, 31, 32, 2, 33, 12, 34, 35, 36, 2, 37, 2, 38, 39, 40, 6, 41, 2, 42, 43, 44, 2, 45, 2, 46, 47, 48, 4, 49, 2, 50, 51, 52, 2, 53, 20, 54, 55, 56, 2, 57, 12, 58, 59, 60, 8, 61, 2, 62, 63, 64, 2

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

OFFSET

1,2

COMMENTS

Restricted growth sequence transform of P(A046523(n), A078898(n)), where P(a,b) is a two-argument form of A000027 used as a Cantor pairing function N x N -> N.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

EXAMPLE

a(10) = a(65) (= 6) because A078898(10) = A078898(65) = 5 (both numbers occur in column 5 of A083221) and because both have the same prime-signature (both are nonsquare semiprimes).

PROG

(PARI)

rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om, invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om, invec[i], i); outvec[i] = u; u++ )); outvec; };

write_to_bfile(start_offset, vec, bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }

A020639(n) = { if(1==n, n, vecmin(factor(n)[, 1])); };

A046523(n) = my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]) \\ From A046523

A064989(n) = {my(f); f = factor(n); if((n>1 && f[1, 1]==2), f[1, 2] = 0); for (i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f)};

A078898(n) = { if(n<=1, n, my(spf=A020639(n), k=1, m=n/spf); while(m>1, if(A020639(m)>=spf, k++); m--); (k)); };

Aux300248(n) = if(1==n, 0, (1/2)*(2 + ((A078898(n)+A046523(n))^2) - A078898(n) - 3*A046523(n)));

write_to_bfile(1, rgs_transform(vector(65537, n, Aux300248(n))), "b300248.txt");

CROSSREFS

Cf. A046523, A078898.

Cf. also A300226, A300229, A300247.

Sequence in context: A300230 A305897 A355834 * A300247 A318887 A305975

Adjacent sequences: A300245 A300246 A300247 * A300249 A300250 A300251

KEYWORD

nonn

AUTHOR

Antti Karttunen, Mar 03 2018

STATUS

approved