A309621 Numbers k such that the number of divisors of k is equal to the number of power-of-two-divisors of the sum of divisors of k.
1, 5, 13, 14, 15, 17, 27, 29, 37, 39, 41, 46, 51, 53, 55, 61, 73, 87, 89, 95, 97, 101, 109, 111, 113, 123, 124, 137, 142, 143, 149, 157, 159, 173, 181, 183, 186, 187, 193, 197, 206, 215, 219, 229, 231, 233, 241, 247, 257, 267, 269, 277, 279, 281, 291, 293, 295, 302, 303, 313, 317, 319, 323
Offset: 1
Examples
14 is in this sequence because it has 4 divisors (1, 2, 7, 14) and 1 + 2 + 7 + 14 = 24 also has 4 power-of-two-divisors 1, 2, 4, 8.
Programs
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Magma
[n: n in [1..300] | NumberOfDivisors(n) eq Valuation(2*SumOfDivisors(n),2)];
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Mathematica
Select[Range[323], DivisorSigma[0, #] == 1 + IntegerExponent[ DivisorSigma[1, #], 2] &] (* Giovanni Resta, Sep 19 2019 *)
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PARI
isA309621(n) = (numdiv(n)==(1+valuation(sigma(n),2))); \\ Antti Karttunen, Aug 12 2019
Comments