A286683 Even numbers k such that the number of odd divisors of k is equal to the 2-adic valuation of k.

2, 12, 20, 28, 44, 52, 68, 72, 76, 92, 116, 124, 148, 164, 172, 188, 200, 212, 236, 240, 244, 268, 284, 292, 316, 332, 336, 356, 388, 392, 404, 412, 428, 432, 436, 452, 508, 524, 528, 548, 556, 560, 596, 604, 624, 628, 652, 668, 692, 716, 724, 764, 772, 788, 796, 816

Offset: 1

Author

Juri-Stepan Gerasimov, Jun 22 2017

Keywords

• nonn
• easy

Comments

This sequence is infinite; 4 * p is in the sequence for odd prime p. - David A. Corneth, Jun 22 2017

Examples

			2 is in this sequence because A001227(2) = A007814(2) = 1.
240 is in the sequence because 240 has 4 odd divisors; they are 1, 3, 5 and 15. Furthermore, 240 = 2^4 * 3 * 5. - _David A. Corneth_, Jun 22 2017
		

Crossrefs

Cf. A001227, A007814, A072978.

Programs

Mathematica

Select[Range@ 820, DivisorSum[#, 1 &, OddQ] == IntegerExponent[#, 2] &] (* Michael De Vlieger, Jun 22 2017 *)

PARI

is(n) = my(v); n%2==0 && v=valuation(n, 2); numdiv(n>>v)==v \\ David A. Corneth, Jun 22 2017

Formula

a(n) = 2*A072978(n).

A001227(a(n)) = A007814(a(n)).

Extensions

More terms from Michael De Vlieger, Jun 22 2017

240 and 336 inserted by David A. Corneth, Jun 22 2017