A327937 Multiplicative with a(p^e) = p^(p-1) if e >= p, otherwise a(p^e) = p^e.

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

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/((p+1)*p^(p-1))) = 0.40498413761092854213... . - Amiram Eldar, Nov 07 2022

Mathematica

f[p_, e_] := If[e >= p, p^(p - 1), p^e]; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Nov 07 2022 *)

Prog

(PARI) A327937(n) = { my(f = factor(n)); for(k=1, #f~, if(f[k, 2]>=f[k, 1], f[k, 2] = f[k, 1]-1)); factorback(f); };

Crossrefs

Cf. A048103, A129251, A327936, A327938.

Sequence in context: A090078 A325814 A325126 * A259445 A080979 A287620

Adjacent sequences: A327934 A327935 A327936 * A327938 A327939 A327940

Keyword

nonn,mult

Author

Antti Karttunen, Oct 01 2019

Status

approved