A054496 - OEIS

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) * ... .

%I #21 Aug 31 2023 05:28:12

%S 1,2,3,16,5,6,7,512,81,10,11,48,13,14,15,65536,17,162,19,80,21,22,23,

%T 1536,625,26,19683,112,29,30,31,33554432,33,34,35,1296,37,38,39,2560,

%U 41,42,43,176,405,46,47,196608,2401,1250,51,208,53,39366,55,3584,57

%N 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) * ... .

%H Reinhard Zumkeller, <a href="/A054496/b054496.txt">Table of n, a(n) for n = 1..10000</a>

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

%p a:= n-> mul(i[1]^(i[2]^2), i=ifactors(n)[2]):

%p seq(a(n), n=1..50); # _Alois P. Heinz_, Jun 09 2014

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

%o (Haskell)

%o a054496 n = product $

%o zipWith (^) (a027748_row n) (map a000290 $ a124010_row n)

%o -- _Reinhard Zumkeller_, Apr 27 2013

%o (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

%Y Cf. A027748, A124010, A000290.

%K nonn,easy,mult

%O 1,2

%A _Leroy Quet_, May 14 2000