

A219302


Numbers having factorization Product_{i=1..m} p(i)^e(i) such that m > 1 and p(i) + e(i) is the same for each i.


2



12, 72, 80, 135, 432, 448, 800, 875, 1701, 2025, 2160, 2592, 6272, 8000, 11264, 15552, 17303, 30375, 30625, 35721, 53248, 56000, 64800, 80000, 87808, 93312, 93347, 108864, 184877, 212625, 216513, 247808, 455625, 559872, 750141, 756059, 800000, 859375
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OFFSET

1,1


LINKS



EXAMPLE

12 = 2^2 * 3^1 and 2+2 = 3+1, so 12 is a term.
64800 = 2^5 * 3^4 * 5^2 and 2+5 = 3+4 = 5+2, so 64800 is a term.
212625 = 3^5 * 5^3 * 7^1 and 3+5 = 5+3 = 7+1, etc.
750141 = 3^7 * 7^3 and 3+7 = 7+3, etc.
The first term with three prime factors is 2160 = 2^4 * 3^3 * 5^1; the first with four is 13608000 = 2^6 * 3^5 * 5^3 * 7^1.


MATHEMATICA

fQ[n_] := Module[{f = FactorInteger[n]}, Length[f] > 1 && Length[Union[Plus @@@ f]] == 1]; Select[Range[2, 100000], fQ] (* T. D. Noe, Nov 21 2012 *)


CROSSREFS

Cf. A219301 (includes primes and prime powers).


KEYWORD

nonn


AUTHOR



STATUS

approved



