A348037 a(n) = n / gcd(n, A003968(n)), where A003968 is multiplicative with a(p^e) = p*(p+1)^(e-1).

1, 1, 1, 2, 1, 1, 1, 4, 3, 1, 1, 2, 1, 1, 1, 8, 1, 3, 1, 2, 1, 1, 1, 4, 5, 1, 9, 2, 1, 1, 1, 16, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 2, 3, 1, 1, 8, 7, 5, 1, 2, 1, 9, 1, 4, 1, 1, 1, 2, 1, 1, 3, 32, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 5, 2, 1, 1, 1, 8, 27, 1, 1, 2, 1, 1, 1, 4, 1, 3, 1, 2, 1, 1, 1, 16, 1, 7, 3, 5, 1, 1, 1, 4, 1

Offset: 1

Author

Antti Karttunen, Oct 19 2021

Keywords

• nonn

Links

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

Crossrefs

Differs from A003557 at the positions given by A347960.

Cf. A003959, A003968, A333634, A348038, A348039, A348499 (positions of 1's).

Programs

Mathematica

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

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); }
A348037(n) = (n/gcd(n, A003968(n)));

Formula

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

a(n) = A003557(n) / A348039(n).