A061345 Odd prime powers.

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

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

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L. J. Corwin, Irreducible polynomials over the integers which factor mod p for every p, Unpublished Bell Labs Memo, Sep 07 1967 [Annotated scanned copy]

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

Cf. A061346, A000961, A005408, A061344, A075109, A075110.

Sequence in context: A082916 A325372 A098903 * A238266 A308838 A080429

Adjacent sequences: A061342 A061343 A061344 * A061346 A061347 A061348

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