A175667 Smallest number m such that phi(m) = n*tau(m), with phi=A000010 and tau=A000005; a(n)=0 if no such m exists.

1, 5, 7, 34, 11, 13, 58, 17, 19, 55, 23, 65, 106, 29, 31, 85, 0, 37, 0, 41, 43, 115, 47, 119, 125, 53, 133, 145, 59, 61, 0, 388, 67, 274, 71, 73, 298, 0, 79, 187, 83, 203, 346, 89, 209, 235, 0, 97, 394, 101, 103, 169, 107, 109, 253, 113, 458, 295, 0, 287, 0, 0, 127, 514, 131

Offset

1,2

Comments

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

From R. J. Mathar, Aug 07 2010: (Start)

First column in the array

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

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

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

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

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

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

58,98,174,294,

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

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

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

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

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

... (End)

Links

Enrique Pérez Herrero, Table of n, a(n) for n = 1..5000

Formula

From Enrique Pérez Herrero, Jan 01 2012: (Start)

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

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

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

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

(End)

Mathematica

Table[SelectFirst[Range[10^5], EulerPhi@ # == n DivisorSigma[0, #] &] /.
k_ /; MissingQ@ k -> 0, {n, 120}] (* Michael De Vlieger, Aug 09 2017, Version 10.2 *)

Crossrefs

Cf. A112954, A112955

Cf. A005384, A023212, A043297.

Sequence in context: A243019 A007911 A066172 * A341063 A018353 A176958

Adjacent sequences: A175664 A175665 A175666 * A175668 A175669 A175670

Keyword

nonn

Author

Enrique Pérez Herrero, Aug 05 2010

Extensions

More terms from R. J. Mathar, Aug 07 2010

Comment corrected by Enrique Pérez Herrero, Aug 12 2010

Status

approved