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A061345
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Odd prime powers.
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33
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1, 3, 5, 7, 9, 11, 13, 17, 19, 23, 25, 27, 29, 31, 37, 41, 43, 47, 49, 53, 59, 61, 67, 71, 73, 79, 81, 83, 89, 97, 101, 103, 107, 109, 113, 121, 125, 127, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239
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OFFSET
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0,2
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COMMENTS
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Let a(n)=p^e, then tau(a(n)^2) = tau(p^(2*e)) = 2*e+1 = 2*(e+1)-1 = tau(2*a(n))-1 where tau=A000005. - Juri-Stepan Gerasimov, Jul 14 2011
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LINKS
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Robert Israel, Table of n, a(n) for n = 0..10000
L. J. Corwin, Irreducible polynomials over the integers which factor mod p for every p, Unpublished Bell Labs Memo, Sep 07 1967 [Annotated scanned copy]
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FORMULA
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a(n) = A061344(n)-1.
Intersection of A000961 (prime powers) and A005408 (odd numbers). - Robert Israel, Jun 11 2014
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MAPLE
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select(t -> nops(ifactors(t)[2])<=1, [seq(2*i+1, i=0..1000)]); # Robert Israel, Jun 11 2014
# alternative:
A061345 := proc(n)
option remember;
local k ;
if n = 0 then
1;
else
for k from procname(n-1)+2 by 2 do
if nops(numtheory[factorset](k)) = 1 then
return k ;
end if;
end do:
end if;
end proc: # R. J. Mathar, Jun 25 2016
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MATHEMATICA
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t={1}; k=0; Do[If[k==1, AppendTo[t, a1]]; k=0; Do[c=Sqrt[a^2+b^2]; If[IntegerQ[c]&&GCD[a, b, c]==1, k++; a1=a; b1=b; c1=c; ], {b, 4, a^2/2, 2}], {a, 3, 260, 2}]; t (* Vladimir Joseph Stephan Orlovsky, Jan 29 2012 *)
Select[2 Range@ 130 - 1, PrimeNu@# < 2 &] (* Robert G. Wilson v, Jun 12 2014 *)
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PROG
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(MAGMA) [1] cat [n: n in [3..300 by 2] | IsPrimePower(n)]; // Bruno Berselli, Feb 25 2016
(PARI) is(n)=my(p); if(isprimepower(n, &p), p>2, n==1) \\ Charles R Greathouse IV, Jun 08 2016
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CROSSREFS
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Cf. A061346, A000961, A005408, A061344.
Sequence in context: A082916 A325372 A098903 * A238266 A308838 A080429
Adjacent sequences: A061342 A061343 A061344 * A061346 A061347 A061348
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane, Jun 08 2001
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), Jun 12 2001
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STATUS
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approved
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