

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
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OFFSET

1,2


COMMENTS

All primes and powers of primes are necessarily in this sequence.


LINKS



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).


KEYWORD

nonn


AUTHOR



STATUS

approved



