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A286683
Even numbers k such that the number of odd divisors of k is equal to the 2-adic valuation of k.
1
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
1,1
COMMENTS
This sequence is infinite; 4 * p is in the sequence for odd prime p. - David A. Corneth, Jun 22 2017
FORMULA
a(n) = 2*A072978(n).
A001227(a(n)) = A007814(a(n)).
EXAMPLE
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
MATHEMATICA
Select[Range@ 820, DivisorSum[#, 1 &, OddQ] == IntegerExponent[#, 2] &] (* Michael De Vlieger, Jun 22 2017 *)
PROG
(PARI) is(n) = my(v); n%2==0 && v=valuation(n, 2); numdiv(n>>v)==v \\ David A. Corneth, Jun 22 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Michael De Vlieger, Jun 22 2017
240 and 336 inserted by David A. Corneth, Jun 22 2017
STATUS
approved