A336596 Numbers whose number of divisors is divisible by 7.

64, 192, 320, 448, 576, 704, 729, 832, 960, 1088, 1216, 1344, 1458, 1472, 1600, 1728, 1856, 1984, 2112, 2240, 2368, 2496, 2624, 2752, 2880, 2916, 3008, 3136, 3264, 3392, 3520, 3645, 3648, 3776, 3904, 4032, 4160, 4288, 4416, 4544, 4672, 4800, 4928, 5056, 5103

Offset

1,1

Comments

The asymptotic density of this sequence is 1 - zeta(7)/zeta(6) = 0.0088404638... (Sathe, 1945).

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Eckford Cohen, Arithmetical Notes, XIII. A Sequal to Note IV, Elemente der Mathematik, Vol. 18 (1963), pp. 8-11.

S. S. Pillai, On a congruence property of the divisor function, J. Indian Math. Soc. (N. S.), Vol. 6, (1942), pp. 118-119.

L. G. Sathe, On a congruence property of the divisor function, American Journal of Mathematics, Vol. 67, No. 3 (1945), pp. 397-406.

Formula

A030516 UNION A030632 UNION A137484 UNION A137491 UNION A175745 UNION A175750 UNION ... - R. J. Mathar, May 05 2023

Example

64 is a term since A000005(64) = 7 is divisible by 7.

Maple

q:= n-> is(irem(numtheory[tau](n), 7)=0):
select(q, [$1..5500])[];  # Alois P. Heinz, Jul 26 2020

Mathematica

Select[Range[5000], Divisible[DivisorSigma[0, #], 7] &]

Crossrefs

Cf. A000005, A008589, A059269, A336595.

Cf. A030516, A113851 and A138031 are subsequences.

Sequence in context: A376204 A045052 A195089 * A175166 A220763 A030028

Adjacent sequences: A336593 A336594 A336595 * A336597 A336598 A336599

Keyword

nonn

Author

Amiram Eldar, Jul 26 2020

Status

approved