A079334 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.

1, 2, 3, 4, 5, 6, 7, 8, 9, 14, 15, 20, 24, 27, 35, 48, 49, 63, 80, 90, 91, 125, 160, 161, 224, 440, 728, 735, 2024, 2400, 2744, 4095, 4374, 12879, 13824, 20735, 30624

Offset

1,2

Comments

No other terms < 212000. - Robert G. Wilson v, Jan 06 2002

No other terms < 30000000. - Dana Jacobsen, Sep 06 2015

Links

Table of n, a(n) for n=1..37.

Eric Weisstein's World of Mathematics, Tau Function.

Mathematica

(* First do <<NumberTheory`Ramanujan` *) test[n_] := Mod[RamanujanTau[n], n]==0; Select[Range[33000], test[ # ]&&test[ #+1]&]

Prog

(PARI) tauvec(N) = Vec(q*eta(q + O(q^N))^24)
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
(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

Crossrefs

Cf. A000594, A063938.

Sequence in context: A334918 A354220 A125506 * A085153 A339111 A130010

Adjacent sequences: A079331 A079332 A079333 * A079335 A079336 A079337

Keyword

nonn,more

Author

Dean Hickerson, Jan 03 2003

Status

approved