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A066872
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p^2 + 1 as p runs through the primes.
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19
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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FORMULA
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MATHEMATICA
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PROG
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(PARI) { for (n=1, 1000, write("b066872.txt", n, " ", prime(n)^2 + 1) ) } \\ Harry J. Smith, Apr 02 2010
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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