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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)).
6
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
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).
Sequence in context: A022157 A065599 A171228 * A318680 A171560 A302451
KEYWORD
nonn,mult
AUTHOR
Antti Karttunen, Oct 23 2019
STATUS
approved