A353792 a(n) = A003958(sigma(n)) * A064989(sigma(n)).

1, 4, 1, 30, 4, 4, 1, 48, 132, 16, 4, 30, 30, 4, 4, 870, 16, 528, 12, 120, 1, 16, 4, 48, 870, 120, 12, 30, 48, 16, 1, 480, 4, 64, 4, 3960, 306, 48, 30, 192, 120, 4, 70, 120, 528, 16, 4, 870, 1224, 3480, 16, 900, 64, 48, 16, 48, 12, 192, 48, 120, 870, 4, 132, 14238, 120, 16, 208, 480, 4, 16, 16, 6336, 1116, 1224, 870

Offset: 1

Author

Antti Karttunen, May 11 2022

Keywords

• nonn
• mult

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• 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. A003958, A064989, A350073, A351442, A353791, A353793, A353794 [= a(A003961(n))].

Cf. A046528 (positions of 1's).

Cf. also A353750.

Programs

PARI

A003958(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]--); factorback(f); };
A064989(n) = { my(f=factor(n>>valuation(n,2))); for(i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f); };
A353792(n) = { my(s=sigma(n)); (A003958(s)*A064989(s)); };

PARI

A353792(n) = { my(f=factor(n),s); prod(i=1, #f~, s = sigma(f[i,1]^f[i,2]); A003958(s)*A064989(s)); };

Formula

Multiplicative with a(p^e) = A003958(1 + p + ... + p^e) * A064989(1 + p + ... + p^e).

a(n) = A353791(A000203(n)).

a(n) = A351442(n) * A350073(n) = A003958(A000203(n)) * A064989(A000203(n)).