A374590 Numbers whose maximum exponent in their prime factorization is an evil number (A001969).

8, 24, 27, 32, 40, 54, 56, 64, 72, 88, 96, 104, 108, 120, 125, 135, 136, 152, 160, 168, 184, 189, 192, 200, 216, 224, 232, 243, 248, 250, 264, 270, 280, 288, 296, 297, 312, 320, 328, 343, 344, 351, 352, 360, 375, 376, 378, 392, 408, 416, 424, 440, 448, 456, 459

Offset: 1

Author

Amiram Eldar, Jul 12 2024

Keywords

• nonn
• easy
• base

Comments

The asymptotic density of this sequence is Sum_{k in A001969} (1/zeta(k+1) - 1/zeta(k)) = 0.12101890210392912747... .

Links

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

Crossrefs

Cf. A001969, A051903.

Subsequence of A013929 and A262675 \ {1}.

Similar sequences: A368714, A369937, A369938, A369939, A374588, A374589.

Programs

Mathematica

evilQ[n_] := EvenQ[DigitCount[n, 2, 1]]; q[n_] := evilQ[Max[FactorInteger[n][[;; , 2]]]]; Select[Range[500], q]

PARI

is(n) = n > 1 && !(hammingweight(vecmax(factor(n)[, 2])) % 2);