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
Keywords
Examples
16 is a term since A000005(16) = 5 is divisible by 5.
References
- G. H. Hardy, Ramanujan: twelve lectures on subjects suggested by his life and work, Cambridge, University Press, 1940, p. 63.
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
Programs
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Maple
q:= n-> is(irem(numtheory[tau](n), 5)=0): select(q, [$1..1300])[]; # Alois P. Heinz, Jul 26 2020
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Mathematica
Select[Range[1300], Divisible[DivisorSigma[0, #], 5] &]
Comments