A343819 Numbers k such that k and k+1 have the same number of Fermi-Dirac factors (A064547).

2, 3, 4, 14, 16, 20, 21, 26, 27, 32, 33, 34, 35, 38, 44, 45, 50, 51, 57, 62, 63, 64, 68, 74, 75, 76, 85, 86, 91, 92, 93, 94, 98, 99, 104, 111, 115, 116, 117, 118, 122, 123, 124, 133, 135, 141, 142, 143, 144, 145, 146, 147, 158, 161, 171, 175, 176, 177, 187, 189

Offset: 1

Author

Amiram Eldar, Apr 30 2021

Keywords

• nonn

Comments

Since the number of infinitary divisors of k is A037445(k) = 2^A064547(k), this is also the sequence of numbers k such that k and k+1 have the same number of infinitary divisors.

Examples

			2 is a term since A064547(2) = A064547(3) = 1.
		

Links

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

Crossrefs

Cf. A064547, A306985, A343818.

Similar sequences: A005237, A006049.

Subsequence of A086263.

Programs

Mathematica

fd[1] = 0; fd[n_] := Plus @@ DigitCount[FactorInteger[n][[;;,2]], 2, 1]; Select[Range[200], fd[#] == fd[# + 1] &]