cp's OEIS Frontend

A336595 Numbers whose number of divisors is divisible by 5.

%I A336595 #14 May 04 2025 03:27:57
%S A336595 16,48,80,81,112,144,162,176,208,240,272,304,324,336,368,400,405,432,
%T A336595 464,496,512,528,560,567,592,624,625,648,656,688,720,752,784,810,816,
%U A336595 848,880,891,912,944,976,1008,1040,1053,1072,1104,1134,1136,1168,1200,1232
%N A336595 Numbers whose number of divisors is divisible by 5.
%C A336595 The asymptotic density of this sequence is 1 - zeta(5)/zeta(4) = 0.0419426259... (Sathe, 1945).
%D A336595 G. H. Hardy, Ramanujan: twelve lectures on subjects suggested by his life and work, Cambridge, University Press, 1940, p. 63.
%H A336595 Amiram Eldar, <a href="/A336595/b336595.txt">Table of n, a(n) for n = 1..10000</a>
%H A336595 Eckford Cohen, <a href="https://eudml.org/doc/140760">Arithmetical Notes, XIII. A Sequal to Note IV</a>, Elemente der Mathematik, Vol. 18 (1963), pp. 8-11.
%H A336595 S. S. Pillai, <a href="https://doi.org/10.18311/jims/1942/17182">On a congruence property of the divisor function</a>, J. Indian Math. Soc. (N. S.), Vol. 6, (1942), pp. 118-119.
%H A336595 L. G. Sathe, <a href="https://www.jstor.org/stable/2371953">On a congruence property of the divisor function</a>, American Journal of Mathematics, Vol. 67, No. 3 (1945), pp. 397-406.
%F A336595 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
%e A336595 16 is a term since A000005(16) = 5 is divisible by 5.
%p A336595 q:= n-> is(irem(numtheory[tau](n), 5)=0):
%p A336595 select(q, [$1..1300])[];  # _Alois P. Heinz_, Jul 26 2020
%t A336595 Select[Range[1300], Divisible[DivisorSigma[0, #], 5] &]
%Y A336595 Cf. A000005, A008587, A059269, A336596.
%Y A336595 Cf. A030514, A030628, A113849, A178739, A179665, A030633, A030638, A137488, A137493, A175745.
%K A336595 nonn
%O A336595 1,1
%A A336595 _Amiram Eldar_, Jul 26 2020