login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Numbers k that do not divide Ramanujan's tau(k).
2

%I #33 Feb 01 2022 00:28:28

%S 11,13,17,19,22,23,26,29,31,33,34,37,38,39,41,43,44,46,47,51,52,53,55,

%T 57,58,59,61,62,65,66,67,68,69,71,73,74,76,77,78,79,82,83,85,86,87,89,

%U 93,94,95,97,99,101,102,103,104,106,107,109,110,111,113,114

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

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

%C Subsequence of A068191.

%C Complement of A063938. - _Omar E. Pol_, Aug 28 2011

%H T. D. Noe, <a href="/A191599/b191599.txt">Table of n, a(n) for n = 1..1000</a>

%H B. Ramakrishnan and Brundaban Sahu, <a href="https://arxiv.org/abs/0711.3512">Rankin-Cohen brackets and Van der Pol-type identities for the Ramanujan's tau function</a>, arXiv:0711.3512 [math.NT], 2007, pp. 14. See Corollary 2.11

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

%p 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;

%t Select[Range[120], !Divisible[RamanujanTau[#], #]&] (* _Jean-François Alcover_, Nov 29 2017 *)

%o (PARI) isok(k) = ramanujantau(k) % k; \\ _Michel Marcus_, Aug 14 2021

%Y Cf. A000594, A068191.

%K nonn

%O 1,1

%A _Luis H. Gallardo_, Jun 08 2011