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A272859 Numbers m such that sigma(Product(p_j)) = sigma(Product(e_j)), where m = Product((p_i)^e_i) and sigma = A000203. 3
1, 4, 27, 72, 108, 192, 800, 1458, 3125, 5120, 6144, 6272, 10976, 12500, 21600, 30375, 36000, 48600, 54675, 77760, 84375, 114688, 116640, 121500, 134456, 138240, 169344, 173056, 225000, 229376, 247808, 337500, 354294, 384000, 395136, 600000, 653184, 655360, 703125, 750141, 823543, 857304, 913952, 979776 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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.

The condition defining this sequence coincides with the condition in A272858 at least for the terms of A114129.

LINKS

Giuseppe Coppoletta and Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 100 terms from G. Coppoletta)

EXAMPLE

173056 is included because 173056 = 2^10 * 13^2 and sigma(2*13) = sigma(10*2).

653184 is included because 653184 = 2^7 * 3^6 * 7 and sigma(2*3*7) = sigma(7*6*1).

MATHEMATICA

Select[Range[10^6], First@ # == Last@ # &@ Map[DivisorSigma[1, Times @@ #] &, Transpose@ FactorInteger@ #] &] (* Michael De Vlieger, May 12 2016 *)

PROG

(Sage) A272859=[]

for n in (1..1000000):

    v=factor(n)[:]; L=len(v)

    if prod((1+v[j][0]) for j in range(L))==sigma(prod(v[j][1] for j in range(L))): A272859.append(n)

print A272859

CROSSREFS

Cf. A048102, A054411, A054412, A071174, A114129, A122406, A272818, A272858.

Sequence in context: A158186 A272858 A272818 * A054412 A122405 A122406

Adjacent sequences:  A272856 A272857 A272858 * A272860 A272861 A272862

KEYWORD

nonn

AUTHOR

Giuseppe Coppoletta, May 08 2016

STATUS

approved

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Last modified July 23 20:32 EDT 2019. Contains 325264 sequences. (Running on oeis4.)