A327938 Multiplicative with a(p^e) = p^(e mod p).

1, 2, 3, 1, 5, 6, 7, 2, 9, 10, 11, 3, 13, 14, 15, 1, 17, 18, 19, 5, 21, 22, 23, 6, 25, 26, 1, 7, 29, 30, 31, 2, 33, 34, 35, 9, 37, 38, 39, 10, 41, 42, 43, 11, 45, 46, 47, 3, 49, 50, 51, 13, 53, 2, 55, 14, 57, 58, 59, 15, 61, 62, 63, 1, 65, 66, 67, 17, 69, 70, 71, 18, 73, 74, 75, 19, 77, 78, 79, 5, 3, 82, 83, 21, 85, 86, 87, 22

Offset: 1

Author

Antti Karttunen, Oct 01 2019

Keywords

• nonn
• mult

Comments

All terms are in A048103.

Links

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

Crossrefs

Cf. A048103, A129251, A327936, A327937, A327939, A327965.

Differs from A065883 for the first time at n=27.

Programs

Mathematica

f[p_, e_] := p^Mod[e, p]; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Nov 07 2022 *)

PARI

A327938(n) = { my(f = factor(n)); for(k=1, #f~, f[k,2] = (f[k,2]%f[k,1])); factorback(f); };

Formula

Multiplicative with a(p^e) = p^(e mod p).

a(n) = n / A327939(n).

For all n, A129251(a(n)) = 0, A327936(a(n)) = 1.

Sum_{k=1..n} a(k) ~ c * n^2, where c = (1/2) * Product_{p prime} (1/(1+1/p^p)) = 0.38559042841678887219... . - Amiram Eldar, Nov 07 2022