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A061345 Odd prime powers. 43
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
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
LINKS
L. J. Corwin, Irreducible polynomials over the integers which factor mod p for every p, Unpublished Bell Labs Memo, Sep 07 1967 [Annotated scanned copy]
FORMULA
a(n) = A061344(n)-1.
Intersection of A000961 (prime powers) and A005408 (odd numbers). - Robert Israel, Jun 11 2014
MAPLE
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
isOddPrimepower := n -> type(n, 'primepower') and not type(n, 'even'):
A061345List := up_to -> select(isOddPrimepower, [`$`(1..up_to)]):
A061345List(240); # Peter Luschny, Feb 02 2023
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
Sequence in context: A082916 A325372 A098903 * A238266 A308838 A080429
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jun 08 2001
EXTENSIONS
More terms from Larry Reeves (larryr(AT)acm.org), Jun 12 2001
STATUS
approved

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Last modified March 29 08:59 EDT 2024. Contains 371268 sequences. (Running on oeis4.)