A354828 Denominators of Dirichlet inverse of fraction A003961(n) / sigma(n).

1, 1, 4, 7, 6, 4, 8, 35, 208, 6, 12, 14, 14, 8, 24, 7595, 18, 208, 20, 3, 32, 12, 24, 7, 1116, 14, 832, 28, 30, 24, 32, 7595, 48, 18, 48, 728, 38, 20, 56, 15, 42, 32, 44, 42, 416, 24, 48, 1519, 3648, 1116, 72, 49, 54, 832, 72, 35, 16, 30, 60, 12, 62, 32, 1664, 33759775, 12, 48, 68, 63, 96, 48, 72, 182, 74, 38, 4464

Offset: 1

Author

Antti Karttunen, Jun 07 2022

Keywords

• nonn
• frac

Links

• Antti Karttunen, Table of n, a(n) 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, A349161, A349162.

Cf. A354827 (denominators).

Cf. also A349628, A354366.

Programs

PARI

up_to = 65537;
A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
DirInverseCorrect(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = (-u[1]*sumdiv(n, d, if(dA354827(n) = (A003961(n)/sigma(n));
vDirInv = DirInverseCorrect(vector(up_to,n,AuxA354827(n)));
A354828(n) = denominator(vDirInv[n]);