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%I #48 Mar 24 2020 03:30:46
%S 1,4,27,72,108,192,800,1458,3125,5120,6144,6272,10976,12500,21600,
%T 30375,36000,48600,54675,77760,84375,114688,116640,121500,134456,
%U 138240,169344,173056,225000,229376,247808,337500,354294,384000,395136,600000,653184,655360,703125,750141,823543,857304,913952,979776
%N Numbers m such that sigma(Product(p_j)) = sigma(Product(e_j)), where m = Product((p_i)^e_i) and sigma = A000203.
%C A048102 is clearly a subsequence, as for any prime p, p^p satisfy the herein condition. Moreover, due to the multiplicativity of the arithmetic function sigma, A122406 is also a subsequence. More generally, if a number is a term, then any permutation of the exponents in its prime factorization (i.e., any permutation of its prime signature) gives also a term.
%C The condition defining this sequence coincides with the condition in A272858 at least for the terms of A114129.
%H Giuseppe Coppoletta and Giovanni Resta, <a href="/A272859/b272859.txt">Table of n, a(n) for n = 1..10000</a> (first 100 terms from G. Coppoletta)
%e 173056 is included because 173056 = 2^10 * 13^2 and sigma(2*13) = sigma(10*2).
%e 653184 is included because 653184 = 2^7 * 3^6 * 7 and sigma(2*3*7) = sigma(7*6*1).
%t Select[Range[10^6], First@ # == Last@ # &@ Map[DivisorSigma[1, Times @@ #] &, Transpose@ FactorInteger@ #] &] (* _Michael De Vlieger_, May 12 2016 *)
%o (Sage)
%o A272859 = []
%o for n in (1..10000):
%o v = factor(n)
%o if prod(1 + w[0] for w in v) == sigma(prod(w[1] for w in v)): A272859.append(n)
%o print(A272859)
%Y Cf. A048102, A054411, A054412, A071174, A114129, A122406, A272818, A272858.
%K nonn
%O 1,2
%A _Giuseppe Coppoletta_, May 08 2016
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