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 A187039 Numbers that have equal counts of even and odd exponents of primes in their factorization. 14
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified April 15 20:47 EDT 2024. Contains 371696 sequences. (Running on oeis4.)