A196225 - OEIS

%I #24 Jan 22 2025 00:08:57

%S 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,

%T 0,60,0,268435456,120,576,0,0,0,3072,0,68719476736,180,900,0,240,0,

%U 4398046511104,0,0,0,5184,0,0,0,0,0,196608,0,960,46656,0,0,360,0,1152921504606846976

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

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

%H Amiram Eldar, <a href="/A196225/b196225.txt">Table of n, a(n) for n = 1..3323</a>

%H Max Alekseyev, <a href="https://oeis.org/wiki/User:Max_Alekseyev/gpscripts#Inversion_of_Multiplicative_Functions">PARI/GP Scripts for Miscellaneous Math Problems: Inversion of Multiplicative Functions</a> (invphi.gp).

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

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

%o (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)

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

%K nonn

%O 1,3

%A _Jaroslav Krizek_, Jan 02 2013

%E a(24) and a(48) corrected by _Amiram Eldar_, Jan 21 2025