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A354828
Denominators of Dirichlet inverse of fraction A003961(n) / sigma(n).
3
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
1,3
PROG
(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(d<n, v[n/d]*u[d], 0)))); (u) }; \\ Compute the Dirichlet inverse of the sequence given in input vector v.
AuxA354827(n) = (A003961(n)/sigma(n));
vDirInv = DirInverseCorrect(vector(up_to, n, AuxA354827(n)));
A354828(n) = denominator(vDirInv[n]);
CROSSREFS
Cf. A354827 (denominators).
Cf. also A349628, A354366.
Sequence in context: A351546 A349162 A351547 * A308366 A056849 A116081
KEYWORD
nonn,frac
AUTHOR
Antti Karttunen, Jun 07 2022
STATUS
approved