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

1,1

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.

Links

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

Example

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

Mathematica

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

Crossrefs

Cf. A064547, A306985, A343818.

Similar sequences: A005237, A006049.

Subsequence of A086263.

Sequence in context: A354075 A344313 A103048 * A140128 A167906 A100998

Adjacent sequences: A343816 A343817 A343818 * A343820 A343821 A343822

Keyword

nonn

Author

Amiram Eldar, Apr 30 2021

Status

approved