A336595 Numbers whose number of divisors is divisible by 5.

16, 48, 80, 81, 112, 144, 162, 176, 208, 240, 272, 304, 324, 336, 368, 400, 405, 432, 464, 496, 512, 528, 560, 567, 592, 624, 625, 648, 656, 688, 720, 752, 784, 810, 816, 848, 880, 891, 912, 944, 976, 1008, 1040, 1053, 1072, 1104, 1134, 1136, 1168, 1200, 1232

Offset

1,1

Comments

The asymptotic density of this sequence is 1 - zeta(5)/zeta(4) = 0.0419426259... (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

A030514 UNION A030628 \ {1} UNION A030633 UNION A030638 UNION A137488 UNION A137493 UNION A175745 UNION A175749 UNION A175752 UNION A175756 UNION ... - R. J. Mathar, May 05 2023

Example

16 is a term since A000005(16) = 5 is divisible by 5.

Maple

q:= n-> is(irem(numtheory[tau](n), 5)=0):
select(q, [$1..1300])[];  # Alois P. Heinz, Jul 26 2020

Mathematica

Select[Range[1300], Divisible[DivisorSigma[0, #], 5] &]

Crossrefs

Cf. A000005, A008587, A059269, A336596.

Cf. A030514, A030628, A113849, A178739, A179665, A030633, A030638, A137488, A137493, A175745.

Sequence in context: A195087 A348882 A130897 * A069084 A084112 A050428

Adjacent sequences: A336592 A336593 A336594 * A336596 A336597 A336598

Keyword

nonn

Author

Amiram Eldar, Jul 26 2020

Status

approved