A054496 If n = p_1^e_1 * p_2^e_2 * p_3^e_3 * ..., p's = distinct primes, e's = positive integers, then a(n) = p_1^(e_1^2) * p_2^(e_2^2) * p_3^(e_3^2) * ... .

1, 2, 3, 16, 5, 6, 7, 512, 81, 10, 11, 48, 13, 14, 15, 65536, 17, 162, 19, 80, 21, 22, 23, 1536, 625, 26, 19683, 112, 29, 30, 31, 33554432, 33, 34, 35, 1296, 37, 38, 39, 2560, 41, 42, 43, 176, 405, 46, 47, 196608, 2401, 1250, 51, 208, 53, 39366, 55, 3584, 57

Offset

1,2

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Example

a(24) = 1536, since 24 = 2^3 * 3^1 and 1536 = 2^(3^2) * 3^(1^2).

Maple

a:= n-> mul(i[1]^(i[2]^2), i=ifactors(n)[2]):
seq(a(n), n=1..50);  # Alois P. Heinz, Jun 09 2014

Mathematica

f[p_, e_] := p^(e^2); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Aug 31 2023 *)

Prog

(Haskell)
a054496 n = product $
            zipWith (^) (a027748_row n) (map a000290 $ a124010_row n)
-- Reinhard Zumkeller, Apr 27 2013
(PARI) a(n) = my(f=factor(n)); for (i=1, #f~, f[i, 2] = f[i, 2]^2); factorback(f); \\ Michel Marcus, Jun 09 2014

Crossrefs

Cf. A027748, A124010, A000290.

Sequence in context: A080749 A070973 A209593 * A351748 A190116 A088447

Adjacent sequences: A054493 A054494 A054495 * A054497 A054498 A054499

Keyword

nonn,easy,mult

Author

Leroy Quet, May 14 2000

Status

approved