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

1,2

Comments

All terms are in A048103.

Links

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

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

Mathematica

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

Prog

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

Crossrefs

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

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

Sequence in context: A366244 A083346 A319652 * A065883 A214392 A071975

Adjacent sequences: A327935 A327936 A327937 * A327939 A327940 A327941

Keyword

nonn,mult

Author

Antti Karttunen, Oct 01 2019

Status

approved