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
Keywords
Examples
For n=1, a(1)=11 since 11 does not divide tau(11) = 534612.
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
Programs
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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;
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Mathematica
Select[Range[120], !Divisible[RamanujanTau[#], #]&] (* Jean-François Alcover, Nov 29 2017 *)
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PARI
isok(k) = ramanujantau(k) % k; \\ Michel Marcus, Aug 14 2021
Comments