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 A309621 Numbers n such that the number of divisors of n is equal to the number of power-of-two-divisors of the sum of divisors of n. 0
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Numbers n such that A000005(n) = A286357(n). - Antti Karttunen, Aug 12 2019 Perfect powers: 1, 27, 1331, 6859, 79507, 205379, 300763, 571787, 1225043, 2248091, 2685619, 4330747, 5735339, 9393931, ... LINKS FORMULA A000005(a(n)) = A001511(A000203(a(n))). EXAMPLE 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. MATHEMATICA Select[Range[323], DivisorSigma[0, #] == 1 + IntegerExponent[ DivisorSigma[1, #], 2] &] (* Giovanni Resta, Sep 19 2019 *) PROG (MAGMA) [n: n in [1..300] | NumberOfDivisors(n) eq Valuation(2*SumOfDivisors(n), 2)]; (PARI) isA309621(n) = (numdiv(n)==(1+valuation(sigma(n), 2))); \\ Antti Karttunen, Aug 12 2019 CROSSREFS Supersequence of A002144. Cf. A000005, A000203, A001511, A001597, A286357, A309530. Sequence in context: A341751 A244435 A134202 * A191382 A291792 A292565 Adjacent sequences:  A309618 A309619 A309620 * A309622 A309623 A309624 KEYWORD nonn,easy AUTHOR Juri-Stepan Gerasimov, Aug 10 2019 STATUS approved

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Last modified July 27 15:49 EDT 2021. Contains 346308 sequences. (Running on oeis4.)