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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
Sequence in context: A084679 A072588 A267117 * A360554 A325241 A072357
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.)