A347118 Möbius transform of A332449.

1, 3, 8, 6, 24, 4, 48, 20, 12, 8, 120, 0, 168, 48, 48, 60, 288, 12, 360, 208, 168, 72, 528, 24, 30, 312, 84, 384, 840, -32, 960, 180, 312, 384, 552, 108, 1368, 792, 912, 480, 1680, -136, 1848, 1008, -54, 912, 2208, 72, 42, 18, 1224, 1200, 2808, -4, 1080, 960, 2232, 1272, 3480, -244, 3720, 2400, 792, 540, 2832, -120

Offset: 1

Author

Antti Karttunen, Aug 21 2021

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A008683, A156552, A332449.

Cf. also A332463, A347115, A347117.

Programs

PARI

A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
A156552(n) = { my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res };
A332449(n) = A005940(1+(3*A156552(n)));
A347118(n) = sumdiv(n,d,moebius(n/d)*A332449(d));

Formula

a(n) = Sum_{d|n} A008683(n/d) * A332449(d).