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 A219301 Numbers having factorization Product_{i=1..m} p(i)^e(i) such that p(i) + e(i) is the same for each i. 2
 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 16, 17, 19, 23, 25, 27, 29, 31, 32, 37, 41, 43, 47, 49, 53, 59, 61, 64, 67, 71, 72, 73, 79, 80, 81, 83, 89, 97, 101, 103, 107, 109, 113, 121, 125, 127, 128, 131, 135, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS All primes and powers of primes are necessarily in this sequence. LINKS T. D. Noe, Table of n, a(n) for n = 1..1000 EXAMPLE 80 = 2^4 * 5^1 and 2+4 = 5+1, so 80 is a term. 101 = 101^1 and 101 + 1 = no other sums due to being prime, so 101 is a term. 128 = 2^7 and 2+7 = no other sums due to being a prime power, so 128 is a term. 135 = 3^3 * 5^1 and 3+3 = 5+1, so 135 is a term. The first term with three unique prime factors is 2160 = 2^4 * 3^3 * 5^1, since 2+4 = 3+3 = 5+1. MATHEMATICA Join[{1}, Select[Range[2, 200], Length[Union[Plus @@@ FactorInteger[#]]] == 1 &] (* T. D. Noe, Nov 21 2012 *) CROSSREFS Cf. A219302 (subset excludes primes and prime powers). Sequence in context: A300273 A353844 A353833 * A326155 A079734 A050730 Adjacent sequences: A219298 A219299 A219300 * A219302 A219303 A219304 KEYWORD nonn AUTHOR Carl R. White, Nov 17 2012 STATUS approved

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Last modified March 2 15:53 EST 2024. Contains 370494 sequences. (Running on oeis4.)