A342028 Numbers k such that k and k+1 both have mutually distinct exponents in their prime factorization (A130091).

1, 2, 3, 4, 7, 8, 11, 12, 16, 17, 18, 19, 23, 24, 27, 28, 31, 40, 43, 44, 47, 48, 49, 52, 53, 63, 67, 71, 72, 75, 79, 80, 88, 96, 97, 98, 103, 107, 108, 112, 116, 124, 127, 135, 136, 147, 148, 151, 152, 162, 163, 171, 172, 175, 188, 191, 192, 199, 207, 211, 223

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Kevser Aktaş and M. Ram Murty, On the number of special numbers, Proceedings - Mathematical Sciences, Vol. 127, No. 3 (2017), pp. 423-430; alternative link.

Bernardo Recamán Santos, Consecutive numbers with mutually distinct exponents in their canonical prime factorization, MathOverflow, Mar 30 2015.

Example

2 is a term since both 2 and 3 have a single exponent (1) in their prime factorization.
5 is not a term since 6 = 2*3 has two equal exponents (1) in its prime factorization.

Mathematica

q[n_] := Length[(e = FactorInteger[n][[;; , 2]])] == Length[Union[e]]; Select[Range[250], q[#] && q[# + 1] &]

Crossrefs

Subsequence of A130091.

Subsequences: A342029, A342030, A342031.

Sequence in context: A188190 A026808 A240767 * A368402 A284937 A271441

Adjacent sequences: A342025 A342026 A342027 * A342029 A342030 A342031

Keyword

nonn

Author

Amiram Eldar, Feb 25 2021

Status

approved