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

Author

Jaroslav Krizek, Jan 02 2013

Keywords

• nonn

Comments

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

Examples

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

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).

Crossrefs

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

Programs

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)

Formula

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

Extensions

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