A360117 Numbers k such that for all their prime factors p, v(p-1) <= v(k-1), where v(n) = A007814(n) is the 2-adic valuation of n.

2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 21, 23, 25, 27, 29, 31, 32, 33, 37, 41, 43, 45, 47, 49, 53, 57, 59, 61, 63, 64, 65, 67, 69, 71, 73, 77, 79, 81, 83, 89, 93, 97, 99, 101, 103, 105, 107, 109, 113, 117, 121, 125, 127, 128, 129, 131, 133, 137, 139, 141, 145, 147, 149, 151, 157, 161, 163, 165, 167

Offset: 1

Author

Antti Karttunen, Feb 10 2023

Keywords

• nonn

Crossrefs

Union of A000040, A000079 \ {1} and A345330 (odd composite terms).

Cf. A007814, A360116 (characteristic function).

Programs

Mathematica

q[n_] := Module[{v = IntegerExponent[n - 1, 2]}, AllTrue[FactorInteger[n][[;; , 1]], IntegerExponent[# - 1, 2] <= v &]]; Select[Range[2, 200], q] (* Amiram Eldar, Feb 10 2023 *)

PARI

isA360117(n) = A360116(n);