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A066872
p^2 + 1 as p runs through the primes.
19
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
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
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
Product_{n>=1} (1 - 1/a(n)) = Pi^2/15 (A182448). - Amiram Eldar, Nov 07 2022
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
KEYWORD
easy,nonn
AUTHOR
Joseph L. Pe, Jan 21 2002
STATUS
approved