A328618 Multiplicative with a(p^e) = p^e if p = 2 or e is a multiple of p, otherwise a(p^e) = p^((p*floor(e/p)) + (2e mod p)).

1, 2, 9, 4, 25, 18, 49, 8, 3, 50, 121, 36, 169, 98, 225, 16, 289, 6, 361, 100, 441, 242, 529, 72, 625, 338, 27, 196, 841, 450, 961, 32, 1089, 578, 1225, 12, 1369, 722, 1521, 200, 1681, 882, 1849, 484, 75, 1058, 2209, 144, 2401, 1250, 2601, 676, 2809, 54, 3025, 392, 3249, 1682, 3481, 900, 3721, 1922, 147, 64, 4225, 2178, 4489, 1156, 4761, 2450, 5041, 24

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Index entries for sequences that are permutations of the natural numbers

Formula

For all n >= 0, A276085(a(A276086(n))) = A328622(n).

Mathematica

a[n_] := Product[{p, e} = pe; If[p == 2 || Divisible[e, p], p^e, p^((p*Floor[e/p]) + Mod[2e, p])], {pe, FactorInteger[n]}];
Array[a, 100] (* Jean-François Alcover, Nov 21 2021 *)

Prog

(PARI) A328618(n) = { my(f = factor(n), m, q); for(k=1, #f~, q = (f[k, 2]\f[k, 1]); m = (f[k, 2]%f[k, 1]); if(m&&(f[k, 1]!=2), f[k, 2] = q*f[k, 1] + ((2*f[k, 2])%f[k, 1]))); factorback(f); };

Crossrefs

Cf. A328619 (inverse permutation).

Cf. A327938, A328617, A328621, A328622.

Sequence in context: A022157 A065599 A171228 * A318680 A171560 A302451

Adjacent sequences: A328615 A328616 A328617 * A328619 A328620 A328621

Keyword

nonn,mult

Author

Antti Karttunen, Oct 23 2019

Status

approved