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%I #27 Aug 29 2021 11:59:28
%S 1,2,3,4,5,6,7,8,9,14,15,20,24,27,35,48,49,63,80,90,91,125,160,161,
%T 224,440,728,735,2024,2400,2744,4095,4374,12879,13824,20735,30624
%N Numbers k such that k divides tau(k) and k+1 divides tau(k+1), where tau(k)=A000594(k) is Ramanujan's tau function; i.e., k and k+1 are in A063938.
%C No other terms < 212000. - _Robert G. Wilson v_, Jan 06 2002
%C No other terms < 30000000. - _Dana Jacobsen_, Sep 06 2015
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TauFunction.html">Tau Function.</a>
%t (* First do <<NumberTheory`Ramanujan` *) test[n_] := Mod[RamanujanTau[n], n]==0; Select[Range[33000], test[ # ]&&test[ #+1]&]
%o (PARI) tauvec(N) = Vec(q*eta(q + O(q^N))^24)
%o v=tauvec(10000); for(n=1,#v-1,if(Mod(v[n],n) == 0 && Mod(v[n+1],n+1) == 0,print1(n", "))) \\ _Dana Jacobsen_, Sep 06 2015
%o (Perl) use ntheory ":all"; my @p = grep { !(ramanujan_tau($_) % $_) } 1..10000; for (0 .. $#p-1) { say $p[$_] if $p[$_]+1 == $p[$_+1] } # _Dana Jacobsen_, Sep 06 2015
%Y Cf. A000594, A063938.
%K nonn,more
%O 1,2
%A _Dean Hickerson_, Jan 03 2003
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