cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A065127 Nonsquares with number of prime factors equal to twice the number of distinct prime factors.

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%I A065127 #17 Jul 05 2023 10:12:53
%S A065127 24,40,54,56,88,104,135,136,152,184,189,232,240,248,250,296,297,328,
%T A065127 336,344,351,360,375,376,424,459,472,488,504,513,528,536,540,560,568,
%U A065127 584,600,621,624,632,664,686,712,756,776,783,792,808,810,816,824,837
%N A065127 Nonsquares with number of prime factors equal to twice the number of distinct prime factors.
%C A065127 Close to A065036 but not the same. One of several quasi-square classes.
%H A065127 Harry J. Smith, <a href="/A065127/b065127.txt">Table of n, a(n) for n = 1..1000</a>
%F A065127 n = prod( p(i)^e(i)) i in [1, k] => sum( e(i)), i in [1, k] == 2k
%e A065127 240=2^4*3*5 so there are 3 distinct prime factors, sum of exponents is 6=2*3 and 240 is not a square so is in the list.
%t A065127 Select[Range[1000],!IntegerQ[Sqrt[#]]&&PrimeOmega[#]==2*PrimeNu[#]&] (* _Harvey P. Dale_, Jul 05 2023 *)
%o A065127 (PARI) n=0; for (m=1, 10^9, if (issquare(m), next); if (bigomega(m) == 2*omega(m), write("b065127.txt", n++, " ", m); if (n==1000, return))) \\ _Harry J. Smith_, Oct 12 2009
%o A065127 (PARI) is(n)=my(f=factor(n)); issquare(n) && bigomega(f)==2*omega(f) \\ _Charles R Greathouse IV_, Oct 15 2015; corrected by _Michel Marcus_, Apr 25 2020
%K A065127 easy,nonn
%O A065127 1,1
%A A065127 _Olivier Gérard_, Nov 14 2001
%E A065127 OFFSET changed from 0 to 1 by _Harry J. Smith_, Oct 11 2009