A196225 Smallest number k such that sigma(tau(k)) = n, or 0 if there is no such k.

1, 0, 2, 4, 0, 16, 6, 64, 0, 0, 0, 12, 36, 4096, 24, 0, 0, 48, 0, 262144, 0, 0, 0, 144, 0, 0, 0, 60, 0, 268435456, 120, 576, 0, 0, 0, 3072, 0, 68719476736, 180, 900, 0, 240, 0, 4398046511104, 0, 0, 0, 5184, 0, 0, 0, 0, 0, 196608, 0, 960, 46656, 0, 0, 360, 0, 1152921504606846976

Offset

1,3

Comments

Smallest number k such that A062069(k) = A000203(A000005(k)) = n, or 0 if there is no such k.

Links

Amiram Eldar, Table of n, a(n) for n = 1..3323

Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems: Inversion of Multiplicative Functions (invphi.gp).

Formula

a(n) = 0 iff A051444(n) = 0.

Example

a(6) = 16 because number 16 is the smallest number k such that sigma(tau(k)) = 6; (tau(16) = 5, sigma(5) = 6).

Prog

(PARI) a(n) = {my(v = invsigma(n), kmin = 0); for(i = 1, #v, k = A005179(v[i]); if(kmin == 0 || k < kmin, kmin = k)); kmin; } \\ Amiram Eldar, Jan 21 2025, using Max Alekseyev's invphi.gp and R. J. Mathar's A005179(n)

Crossrefs

Cf. A062069 (sigma(tau(n))), A000203(sigma(n)), A000005(tau(n)), A005179, A051444.

Sequence in context: A203850 A106603 A059057 * A127511 A321956 A173315

Adjacent sequences: A196222 A196223 A196224 * A196226 A196227 A196228

Keyword

nonn,changed

Author

Jaroslav Krizek, Jan 02 2013

Extensions

a(24) and a(48) corrected by Amiram Eldar, Jan 21 2025

Status

approved