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 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. 7
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified May 16 21:28 EDT 2021. Contains 343951 sequences. (Running on oeis4.)