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 A066872 p^2 + 1 as p runs through the primes. 11
 5, 10, 26, 50, 122, 170, 290, 362, 530, 842, 962, 1370, 1682, 1850, 2210, 2810, 3482, 3722, 4490, 5042, 5330, 6242, 6890, 7922, 9410, 10202, 10610, 11450, 11882, 12770, 16130, 17162, 18770, 19322, 22202, 22802, 24650, 26570, 27890, 29930, 32042 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS From R. J. Mathar, Aug 28 2011: (Start) There are at least three "natural" embeddings of this function into multiplicative functions b(n), c(n) and d(n): (i) The first is b(n) = 1, 5, 10, 0, 26, 0, 50, ... (n>=1) with b(p) = p^2+1, b(p^e)=0 if e>=2, substituting zero for all composite n. (ii) The second is c(n) = 1, 5, 10, 9, 26, 50, 50, 17, 28, 130, ... (n>=1) with c(p^e)= p^(e+1)+1. (iii) The third is d(n) = 1, 5, 10, 5, 26, 50, 50, 5, 10, 130, ... (n>=1) with d(p^e) = p^2+1 if e>=1. (End) For n > 1, a(n)/2 is of the form 4*k+1. - Altug Alkan, Apr 08 2016 LINKS Harry J. Smith, Table of n, a(n) for n = 1..1000 R. P. Boas & N. J. A. Sloane, Correspondence, 1974 FORMULA a(n) = A002522(A000040(n)). - Altug Alkan, Apr 08 2016 a(n) = A000010(A000040(n)^2) + A323599(A000040(n)^2). - Torlach Rush, Jan 25 2019 MATHEMATICA Table[Prime[n]^2 + 1, {n, 41}] (* Vladimir Joseph Stephan Orlovsky, Mar 11 2009 *) PROG (PARI) { for (n=1, 1000, write("b066872.txt", n, " ", prime(n)^2 + 1) ) } \\ Harry J. Smith, Apr 02 2010 (MAGMA) [p^2+1: p in PrimesUpTo(300)]; // Vincenzo Librandi, Oct 31 2014 CROSSREFS Cf. A002522, A000010, A000040, A323599. Sequence in context: A324005 A166388 A290055 * A301537 A063478 A128665 Adjacent sequences:  A066869 A066870 A066871 * A066873 A066874 A066875 KEYWORD easy,nonn AUTHOR Joseph L. Pe, Jan 21 2002 STATUS approved

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Last modified January 21 22:47 EST 2020. Contains 331129 sequences. (Running on oeis4.)