A187039 Numbers that have equal counts of even and odd exponents of primes in their factorization.
1, 12, 18, 20, 28, 44, 45, 48, 50, 52, 63, 68, 72, 75, 76, 80, 92, 98, 99, 108, 112, 116, 117, 124, 147, 148, 153, 162, 164, 171, 172, 175, 176, 188, 192, 200, 207, 208, 212, 236, 242, 244, 245, 261, 268, 272, 275, 279, 284, 288, 292, 304, 316, 320, 325, 332
Offset: 1
Keywords
Examples
108 = 2^2*3^3 has one even and one odd exponent in its factorization and therefore qualifies.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Zak Seidov)
Programs
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Magma
IsA187039:=func< n | #[ a: a in P | IsEven(a) ] eq #[ a: a in P | IsOdd(a) ] where P is [ g[2]: g in F ] where F is Factorization(n) >; [ n: n in [1..500] | IsA187039(n) ]; // Klaus Brockhaus, Mar 04 2011
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Mathematica
Reap[Do[fi=FactorInteger[n];la=Mod[Last/@fi,2];If[Count[la,1]==Count[la,0],Sow[n]] ,{n,1,10000}]][[2,1]] (* Zak Seidov, Mar 04 2011 *) eoeQ[n_]:=Module[{f=FactorInteger[n][[All,2]]},Count[ f,?OddQ]== Length[ f]/2]; Join[{1},Select[Range[400],eoeQ]] (* _Harvey P. Dale, Sep 23 2016 *)
Comments