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A066885
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(Prime(n)^2+1)/2.
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10
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5, 13, 25, 61, 85, 145, 181, 265, 421, 481, 685, 841, 925, 1105, 1405, 1741, 1861, 2245, 2521, 2665, 3121, 3445, 3961, 4705, 5101, 5305, 5725, 5941, 6385, 8065, 8581, 9385, 9661, 11101, 11401, 12325, 13285, 13945, 14965, 16021, 16381, 18241, 18625
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,1
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COMMENTS
| a(n) is the average of the numbers from 1 to p(n)^2. It's also the average of the primes in a p(n) by p(n) example of Haga's conjecture (see link below).
If a(n) is a square c^2, then p(n) is a NSW prime (A088165) and a prime RMS number (A140480). [From Ctibor O. Zizka (ctibor.zizka(AT)seznam.cz), Aug 26 2008]
The sequence starts with a(2) = (3^2+1)/2 = 5 since a(1) would be (2^2+1)/2 = 5/2. [From Michael Porter (michael_b_porter(AT)yahoo.com), Dec 14 2009]
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LINKS
| Harry J. Smith, Table of n, a(n) for n = 2..1000
Carlos Rivera, The prime puzzles & problems connection, conjecture 26
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FORMULA
| a(n) = 1+A084921(n). - R. J. Mathar, Sep 30 2011
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MATHEMATICA
| a[n_] := (Prime[n]^2+1)/2
lst={}; Do[AppendTo[lst, (DivisorSigma[2, Prime[n]])/2], {n, 2, 5!}]; lst (* From Vladimir Orlovsky (4vladimir(AT)gmail.com), Mar 11 2009 *)
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PROG
| (PARI) A066885(n) = (prime(n)^2+1)/2 [From Michael Porter (michael_b_porter(AT)yahoo.com), Dec 14 2009]
(PARI) { for (n=2, 1000, write("b066885.txt", n, " ", (prime(n)^2 + 1)/2) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Apr 04 2010]
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CROSSREFS
| Cf. A066883, A066886.
Sequence in context: A146140 A146283 A026373 * A147151 A057288 A107466
Adjacent sequences: A066882 A066883 A066884 * A066886 A066887 A066888
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KEYWORD
| easy,nonn
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AUTHOR
| Enoch Haga (Enokh(AT)comcast.net), Jan 22 2002
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EXTENSIONS
| Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Jun 08 2002
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