A349634 Denominators of the Möbius transform of ratio A003961(n)/n.

1, 2, 3, 4, 5, 3, 7, 8, 9, 5, 11, 2, 13, 7, 15, 16, 17, 9, 19, 10, 21, 11, 23, 4, 25, 13, 27, 7, 29, 15, 31, 32, 33, 17, 35, 6, 37, 19, 39, 20, 41, 21, 43, 22, 9, 23, 47, 8, 49, 25, 51, 13, 53, 27, 55, 14, 57, 29, 59, 5, 61, 31, 63, 64, 65, 33, 67, 34, 23, 35, 71, 4, 73, 37, 75, 19, 77, 39, 79, 40, 81, 41, 83, 7

Offset: 1

Author

Antti Karttunen, Nov 28 2021

Keywords

• nonn
• frac

Comments

See comments in A349633.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A000010, A003961, A003972, A008683, A349633 (numerators).

Cf. also A349628.

Programs

Mathematica

f[p_, e_] := NextPrime[p]^e; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; a[n_] := Denominator @ DivisorSum[n, MoebiusMu[n/#] * s[#]/# &]; Array[a, 100] (* Amiram Eldar, Nov 28 2021 *)

PARI

A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
A349634(n) = denominator(sumdiv(n,d,moebius(n/d)*(A003961(d)/d)));