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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.
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%I #8 Feb 10 2023 17:11:30

%S 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,

%T 49,53,57,59,61,63,64,65,67,69,71,73,77,79,81,83,89,93,97,99,101,103,

%U 105,107,109,113,117,121,125,127,128,129,131,133,137,139,141,145,147,149,151,157,161,163,165,167

%N 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.

%t 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 *)

%o (PARI) isA360117(n) = A360116(n);

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

%Y Cf. A007814, A360116 (characteristic function).

%K nonn

%O 1,1

%A _Antti Karttunen_, Feb 10 2023