%I #28 Aug 12 2017 12:46:43

%S 1,5,7,34,11,13,58,17,19,55,23,65,106,29,31,85,0,37,0,41,43,115,47,

%T 119,125,53,133,145,59,61,0,388,67,274,71,73,298,0,79,187,83,203,346,

%U 89,209,235,0,97,394,101,103,169,107,109,253,113,458,295,0,287,0,0,127,514,131

%N Smallest number m such that phi(m) = n*tau(m), with phi=A000010 and tau=A000005; a(n)=0 if no such m exists.

%C If p = 2*n+1 is a prime, and if n > 1 then a(n)=p.

%C From _R. J. Mathar_, Aug 07 2010: (Start)

%C First column in the array

%C 1,3,8,10,18,24,30: A020488

%C 5,9,15,28,40,72,84,90,120: A062516

%C 7,21,26,56,70,78,108,126,168,210: A063469

%C 34,45,52,102,140,156,252,360,420: A063470

%C 11,33,88,110,198,264,330,

%C 13,35,39,63,76,104,105,130,228,234,280,312,390,504,540,630,840,

%C 58,98,174,294,

%C 17,51,128,136,170,176,224,260,306,384,408,468,510,528,672,780,1260,

%C 19,57,74,135,152,182,190,222,342,456,546,570,756,1080,

%C 55,82,99,124,165,246,308,350,372,440,792,924,990,1050,1320,

%C 23,69,184,230,414,552,690,

%C 65,117,148,195,238,315,364,380,444,520,684,714,864,936,1092,1140,1170,1560,2520,

%C ... (End)

%H Enrique Pérez Herrero, <a href="/A175667/b175667.txt">Table of n, a(n) for n = 1..5000</a>

%F From _Enrique Pérez Herrero_, Jan 01 2012: (Start)

%F If n > 1 then a(n) >= 2*n+1 or a(n)=0.

%F If p and q = 2*p+1 are both prime, A005384, then a(p) = 2*p+1.

%F If p > 3 and q = 4*p+1 are both prime, A023212, then a(p) = 8*p + 2 = 2*q.

%F If p > 2 is prime and both 2*p+1 and 4*p+1 are composite, A043297, then a(n)=0.

%F (End)

%t Table[SelectFirst[Range[10^5], EulerPhi@ # == n DivisorSigma[0, #] &] /.

%t k_ /; MissingQ@ k -> 0, {n, 120}] (* _Michael De Vlieger_, Aug 09 2017, Version 10.2 *)

%Y Cf. A112954, A112955

%Y Cf. A005384, A023212, A043297.

%K nonn

%O 1,2

%A _Enrique Pérez Herrero_, Aug 05 2010

%E More terms from _R. J. Mathar_, Aug 07 2010

%E Comment corrected by _Enrique Pérez Herrero_, Aug 12 2010