A191599 Numbers k that do not divide Ramanujan's tau(k).

11, 13, 17, 19, 22, 23, 26, 29, 31, 33, 34, 37, 38, 39, 41, 43, 44, 46, 47, 51, 52, 53, 55, 57, 58, 59, 61, 62, 65, 66, 67, 68, 69, 71, 73, 74, 76, 77, 78, 79, 82, 83, 85, 86, 87, 89, 93, 94, 95, 97, 99, 101, 102, 103, 104, 106, 107, 109, 110, 111, 113, 114

Offset

1,1

Comments

This sequence has its first 45 terms in common with A068191.

Subsequence of A068191.

Complement of A063938. - Omar E. Pol, Aug 28 2011

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

B. Ramakrishnan and Brundaban Sahu, Rankin-Cohen brackets and Van der Pol-type identities for the Ramanujan's tau function, arXiv:0711.3512 [math.NT], 2007, pp. 14. See Corollary 2.11

Example

For n=1, a(1)=11 since 11 does not divide tau(11) = 534612.

Maple

with(numtheory): tn := proc(n) modp(-840*sum(k^4*sigma(k)*sigma(n-k), k=1..n-1), n); end; ser := proc(a, b) local n, lis; lis := []; for n from a to b do if tn(n) <> 0 then lis := [op(lis), n]; fi; od; lis; end;

Mathematica

Select[Range[120], !Divisible[RamanujanTau[#], #]&] (* Jean-François Alcover, Nov 29 2017 *)

Prog

(PARI) isok(k) = ramanujantau(k) % k; \\ Michel Marcus, Aug 14 2021

Crossrefs

Cf. A000594, A068191.

Sequence in context: A333237 A048388 A068191 * A084374 A063193 A056758

Adjacent sequences: A191596 A191597 A191598 * A191600 A191601 A191602

Keyword

nonn

Author

Luis H. Gallardo, Jun 08 2011

Status

approved