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 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1000 terms from Donovan Johnson) 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). Sequence in context: A169725 A362518 A209447 * A338261 A101523 A340302 Adjacent sequences: A219299 A219300 A219301 * A219303 A219304 A219305 KEYWORD nonn AUTHOR Carl R. White, Nov 17 2012 STATUS approved

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Last modified February 22 16:01 EST 2024. Contains 370256 sequences. (Running on oeis4.)