A219301 Numbers having factorization Product_{i=1..m} p(i)^e(i) such that p(i) + e(i) is the same for each i.

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

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