A346240 Difference between A341512 and its Möbius transform.

0, 0, 0, 1, 0, 3, 0, 11, 2, 3, 0, 46, 0, 5, 4, 85, 0, 80, 0, 68, 6, 3, 0, 398, 2, 5, 46, 130, 0, 209, 0, 575, 4, 3, 6, 981, 0, 5, 6, 640, 0, 397, 0, 182, 164, 7, 0, 2830, 4, 150, 4, 280, 0, 1435, 4, 1250, 6, 3, 0, 2586, 0, 7, 292, 3661, 6, 551, 0, 368, 8, 507, 0, 7983, 0, 5, 212, 502, 6, 847, 0, 4700, 788, 3, 0, 5078, 4, 5, 4, 1894

Offset: 1

Author

Antti Karttunen, Jul 13 2021

Keywords

• nonn
• look

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A003961, A008683, A341528, A341529, A341512, A346239.

Cf. also A347097.

Programs

PARI

A003961(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From A003961
A341528(n) = (n*sigma(A003961(n)));
A341529(n) = (sigma(n)*A003961(n));
A341512(n) = (A341529(n)-A341528(n));
A346240(n) = -sumdiv(n,d,(dA341512(d));

Formula

a(n) = -Sum_{d|n, dA008683(n/d) * A341512(d).

a(n) = A341512(n) - A346239(n).