A347122 Möbius transform of A347121.

-1, 2, 3, 10, 3, 24, 5, 38, 29, 36, 3, 90, 5, 56, 61, 130, 3, 152, 5, 138, 95, 72, 7, 306, 57, 92, 187, 214, 3, 292, 7, 422, 121, 108, 139, 550, 5, 128, 155, 474, 3, 452, 5, 282, 403, 160, 7, 990, 145, 348, 181, 358, 7, 856, 173, 734, 215, 180, 3, 1046, 7, 208, 625, 1330, 223, 604, 5, 426, 269, 700, 3, 1838, 7, 236

Offset: 1

Author

Antti Karttunen, Aug 24 2021

Keywords

• sign

Links

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

Crossrefs

Cf. A000010, A001223, A003961, A008683, A347121, A347136, A347137.

Programs

PARI

A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A347121(n) = (sumdiv(n,d,d*A003961(n/d))-(2*n));
A347122(n) = sumdiv(n,d,moebius(n/d)*A347121(d));

Formula

a(n) = Sum_{d|n} A008683(n/d) * A347121(d).

a(n) = A347137(n) - 2*A000010(n).

For all n >= 1, a(A000040(n)) = 1 + A001223(n).