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.

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

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