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
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