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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

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

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