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

1,2

Comments

Numbers k such that A000005(k) = A286357(k). - Antti Karttunen, Aug 12 2019

Perfect powers: 1, 27, 1331, 6859, 79507, 205379, 300763, 571787, 1225043, 2248091, 2685619, 4330747, 5735339, 9393931, ...

Links

Table of n, a(n) for n=1..63.

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