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A066872 p^2 + 1 as p runs through the primes. 16
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
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
Sequence in context: A324005 A166388 A290055 * A301537 A063478 A128665
KEYWORD
easy,nonn
AUTHOR
Joseph L. Pe, Jan 21 2002
STATUS
approved

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Last modified March 19 06:19 EDT 2024. Contains 370953 sequences. (Running on oeis4.)