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

1,2

Comments

Numbers k such that A162641(k) = A162642(k). - Amiram Eldar, Sep 27 2021

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Zak Seidov)

Example

108 = 2^2*3^3 has one even and one odd exponent in its factorization and therefore qualifies.

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 *)

Prog

(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

Crossrefs

Cf. A162641, A162642.

Sequence in context: A084679 A072588 A267117 * A360554 A325241 A072357

Adjacent sequences: A187036 A187037 A187038 * A187040 A187041 A187042

Keyword

nonn

Author

Vladimir Shevelev, Mar 02 2011

Status

approved