A319703 a(n) = A003415(A252463(n)).

0, 0, 1, 1, 1, 1, 1, 4, 4, 1, 1, 5, 1, 1, 5, 12, 1, 6, 1, 7, 7, 1, 1, 16, 6, 1, 12, 9, 1, 8, 1, 32, 9, 1, 8, 21, 1, 1, 13, 24, 1, 10, 1, 13, 16, 1, 1, 44, 10, 10, 15, 15, 1, 27, 10, 32, 19, 1, 1, 31, 1, 1, 24, 80, 14, 14, 1, 19, 21, 12, 1, 60, 1, 1, 21, 21, 12, 16, 1, 68, 32, 1, 1, 41, 16, 1, 25, 48, 1, 39, 16, 25, 31, 1

Offset: 1

Author

Antti Karttunen, Nov 22 2018

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A003415, A252463.

Cf. also A319699, A319700, A319989, A320107, A320111.

Programs

PARI

A003415(n) = {my(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1]))}; \\ From A003415
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)};
A252463(n) = if(!(n%2),n/2,A064989(n));
A319703(n) = A003415(A252463(n));

Formula

a(n) = A003415(A252463(n)).