A351445 a(n) = A003958(sigma(n)) - A003958(n), where A003958 is multiplicative with a(p^e) = (p-1)^e and sigma is the sum of divisors function.

0, 1, -1, 5, -2, 0, -5, 7, 8, 0, -8, 4, -6, -4, -6, 29, -12, 20, -14, 8, -11, -6, -20, 6, 14, 0, -4, 0, -20, -4, -29, 23, -18, -8, -22, 68, -18, -10, -18, 12, -28, -10, -32, 2, 8, -18, -44, 28, 0, 44, -28, 24, -44, 0, -36, 2, -32, -12, -50, 4, -30, -28, -12, 125, -36, -16, -50, 8, -42, -20, -66, 92, -36, 0

Offset: 1

Author

Antti Karttunen, Feb 12 2022

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A003958, A351442, A351444, A351457 [= a(A003961(n))].

Cf. A351446 (positions of zeros), A351443 (odd terms there).

Cf. also A348736.

Programs

PARI

A003958(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]--); factorback(f); };
A351445(n) = (A003958(sigma(n)) - A003958(n));

Formula

a(n) = A351442(n) - A003958(n) = A351444(n) - n.