A188540 Numbers k such that d(k+2) = 2*d(k) where d(k) is the number of divisors of k (A000005).

1, 13, 19, 22, 31, 37, 38, 53, 67, 83, 86, 89, 109, 113, 124, 127, 131, 133, 134, 139, 148, 157, 169, 181, 187, 199, 211, 233, 251, 253, 257, 263, 292, 293, 295, 307, 310, 317, 326, 328, 337, 338, 343, 353, 355, 361, 376, 379, 389, 401, 406, 409, 412, 422, 427, 438, 443, 449, 453

Offset: 1

Author

Juri-Stepan Gerasimov, Apr 03 2011

Keywords

• nonn
• easy

Examples

			1 is a term since d(1+2) = d(3) = 2 = 2*d(1).
		

Links

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

Crossrefs

Cf. A000005, A063446, A160921.

Programs

Mathematica

Select[Range[500], DivisorSigma[0, # + 2] == 2 * DivisorSigma[0, #] &] (* Amiram Eldar, Jan 17 2021 *)
Position[Partition[DivisorSigma[0,Range[500]],3,1],?(2#[[1]]== #[[3]]&),1,Heads-> False]// Flatten (* _Harvey P. Dale, Oct 19 2021 *)

PARI

isok(k) = numdiv(k+2) == 2*numdiv(k); \\ Michel Marcus, Jan 17 2021