A379779 Numbers k >= 1 such that A007088(k) / A007088(A007953(k)) is an integer.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 20, 24, 27, 30, 36, 40, 45, 48, 54, 60, 63, 70, 72, 80, 90, 100, 102, 108, 110, 111, 112, 114, 120, 126, 132, 133, 144, 150, 152, 153, 156, 180, 190, 192, 195, 200, 201, 204, 210, 216, 220, 222, 224, 228, 240, 252, 264, 266, 288, 300, 306, 312, 315, 320

Offset: 1

Author

Ctibor O. Zizka, Jan 15 2025

Keywords

• nonn
• base

Examples

			k = 18: A007088(18)/A007088(A007953(18)) = 10010/1001 = 10, thus k = 18 is a member of the sequence.
		

Crossrefs

Cf. A005349, A007088, A007953.

Programs

Mathematica

q[k_] := Divisible @@ (FromDigits[IntegerDigits[#, 2]] & /@ {k, DigitSum[k]}); Select[Range[320], q] (* Amiram Eldar, Jan 15 2025 *)

PARI

bin(n) = fromdigits(binary(n), 10); \\ A007088
isok(k) = denominator(bin(k)/bin(sumdigits(k))) == 1; \\ Michel Marcus, Jan 15 2025