A348038 a(n) = A003968(n) / gcd(n, A003968(n)), where A003968 is multiplicative with a(p^e) = p*(p+1)^(e-1).

1, 1, 1, 3, 1, 1, 1, 9, 4, 1, 1, 3, 1, 1, 1, 27, 1, 4, 1, 3, 1, 1, 1, 9, 6, 1, 16, 3, 1, 1, 1, 81, 1, 1, 1, 2, 1, 1, 1, 9, 1, 1, 1, 3, 4, 1, 1, 27, 8, 6, 1, 3, 1, 16, 1, 9, 1, 1, 1, 3, 1, 1, 4, 243, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 6, 3, 1, 1, 1, 27, 64, 1, 1, 3, 1, 1, 1, 9, 1, 4, 1, 3, 1, 1, 1, 81, 1, 8, 4, 9, 1

Offset

1,4

Links

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

Formula

a(n) = A003968(n) / A348036(n) = A003968(n) / gcd(n, A003968(n)).

a(n) = A327564(n) / A348039(n).

Mathematica

f[p_, e_] := p*(p + 1)^(e - 1); a[n_] := (m = Times @@ f @@@ FactorInteger[n]) / GCD[n, m]; Array[a, 100] (* Amiram Eldar, Oct 20 2021 *)

Prog

(PARI)
A003968(n) = {my(f=factor(n)); for (i=1, #f~, p= f[i, 1]; f[i, 1] = p*(p+1)^(f[i, 2]-1); f[i, 2] = 1); factorback(f); }
A348038(n) = { my(u=A003968(n)); (u/gcd(n, u)); };

Crossrefs

Differs from A327564 at the positions given by A347960.

Cf. A003968, A005117 (positions of 1's), A327564, A348036, A348037, A348039.

Sequence in context: A156535 A365427 A366787 * A327564 A243748 A340149

Adjacent sequences: A348035 A348036 A348037 * A348039 A348040 A348041

Keyword

nonn

Author

Antti Karttunen, Oct 20 2021

Status

approved