A372944 Numbers k that divide the k-th tangent (or "zag") number.

1, 2, 4, 8, 16, 32, 64, 68, 128, 256, 512, 592, 1024, 1156, 2048, 2056, 4096, 4112, 8192, 8224, 8576, 10928, 16384, 16448, 19652, 20512, 28936, 32768, 37888, 41024, 43882, 64804, 65536, 82048

Offset: 1

Author

Amiram Eldar, May 17 2024

Keywords

• nonn
• more

Comments

Numbers k such that k | A000182(k).

All the powers of 2 are terms.

Examples

			2 is a term since A000182(2) = 2 is divisible by 2.
4 is a term since A000182(4) = 272 = 4 * 68 is divisible by 4.
		

Crossrefs

Cf. A000182.

Similar sequences: A014847 (Catalan), A016089 (Lucas), A023172 (Fibonacci), A051177 (partition), A232570 (tribonacci), A246692 (Pell), A266969 (Motzkin).

Programs

Mathematica

Select[Range[1000], Divisible[((-4)^# - (-16)^#) * BernoulliB[2*#]/(2*#), #] &]

PARI

is(n) = (((-4)^n - (-16)^n) * bernfrac(2*n) / (2*n)) % n == 0;