A336852 a(n) = sigma(A003961(n)) - sigma(n).

0, 1, 2, 6, 2, 12, 4, 25, 18, 14, 2, 50, 4, 24, 24, 90, 2, 85, 4, 62, 40, 20, 6, 180, 26, 30, 116, 100, 2, 120, 6, 301, 36, 26, 48, 312, 4, 36, 52, 230, 2, 192, 4, 98, 170, 48, 6, 602, 76, 135, 48, 136, 6, 504, 40, 360, 64, 38, 2, 456, 6, 56, 268, 966, 60, 192, 4, 134, 84, 240, 2, 1045, 6, 54, 218, 172, 72, 264, 4, 782

Offset: 1

Author

Antti Karttunen, Aug 05 2020

Keywords

• nonn

Comments

Inverse Möbius transform of A336853(n) = (A003961(n) - n).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16383
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A003961, A003973, A286385, A336851, A336853.

Cf. A001105 (positions of odd terms), A001359 (positions of 2's).

Programs

PARI

A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A336852(n) = (sigma(A003961(n)) - sigma(n));

PARI

A336852(n) = sumdiv(n,d,A003961(d)-d);

Formula

a(n) = Sum_{d|n} (A003961(d)-d).

a(n) = A003973(n) - A000203(n) = A000203(A003961(n)) - A000203(n).

a(n) = A336851(n) + A286385(n).