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A061346 Odd numbers that are neither primes nor prime powers.

%I A061346 #60 Mar 16 2025 14:50:11
%S A061346 15,21,33,35,39,45,51,55,57,63,65,69,75,77,85,87,91,93,95,99,105,111,
%T A061346 115,117,119,123,129,133,135,141,143,145,147,153,155,159,161,165,171,
%U A061346 175,177,183,185,187,189,195,201,203,205,207,209,213,215,217,219,221
%N A061346 Odd numbers that are neither primes nor prime powers.
%C A061346 Odd numbers with at least two distinct prime factors. - _N. J. A. Sloane_, Oct 15 2022
%C A061346 Odd leg of more than one primitive Pythagorean triangles. For smallest odd leg common to 2^n PPTs, see A070826. - _Lekraj Beedassy_, Jul 12 2006
%C A061346 Numbers that can be factored by Shor's algorithm. - _Charles R Greathouse IV_, Mar 05 2012
%H A061346 Charles R Greathouse IV, <a href="/A061346/b061346.txt">Table of n, a(n) for n = 1..10000</a>
%F A061346 a(n) ~ 2n. - _Charles R Greathouse IV_, Aug 20 2012
%p A061346 select(t -> nops(ifactors(t)[2]) > 1, [seq(2*i+1,i=1..1000)]); # _Robert Israel_, Dec 14 2014
%t A061346 Select[Range[1, 249, 2], Length[FactorInteger[#]] > 1 &] (* _Alonso del Arte_, Jan 30 2012 *)
%t A061346 Select[ Range[1, 475, 2], PrimeNu@# > 1 &] (* _Robert G. Wilson v_, Dec 12 2014 *)
%o A061346 (ARIBAS) for k := 3 to 253 by 2 do ar := factorlist(k); if ar[0] < ar[length(ar)-1] then write(k," ") end; end;
%o A061346 (PARI) is(n)=ispower(n,,&n);n%2&&!isprime(n)&&n>1 \\ _Charles R Greathouse IV_, Jan 30 2012
%o A061346 (PARI) is(n)=n%2 && !isprimepower(n) && n>1 \\ _Charles R Greathouse IV_, May 06 2016
%o A061346 (PARI) count(x)=if(x<9, 0, (x\=1) - sum(k=1,logint(x,3), primepi(sqrtnint(x,k)) - 1) - x\2 - 1) \\ _Charles R Greathouse IV_, Mar 06 2018
%Y A061346 A225375 is a subsequence.
%Y A061346 Cf. A061345.
%K A061346 nonn,easy
%O A061346 1,1
%A A061346 _N. J. A. Sloane_, Jun 08 2001
%E A061346 More terms from _Klaus Brockhaus_, Jun 10 2001