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

Author

Amiram Eldar, Jul 26 2020

Keywords

• nonn

Comments

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

Examples

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

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.

Crossrefs

Cf. A000005, A008589, A059269, A336595.

Cf. A030516, A113851 and A138031 are subsequences.

Programs

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] &]

Formula

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