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.

A321193 Even numbers with no more than one odd prime factor, not counting multiplicity.

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%I A321193 #18 Dec 13 2021 21:19:40
%S A321193 2,4,6,8,10,12,14,16,18,20,22,24,26,28,32,34,36,38,40,44,46,48,50,52,
%T A321193 54,56,58,62,64,68,72,74,76,80,82,86,88,92,94,96,98,100,104,106,108,
%U A321193 112,116,118,122,124,128,134,136,142,144,146,148,152,158,160,162,164,166,172,176,178,184,188,192,194,196
%N A321193 Even numbers with no more than one odd prime factor, not counting multiplicity.
%H A321193 Charles R Greathouse IV, <a href="/A321193/b321193.txt">Table of n, a(n) for n = 1..10000</a>
%F A321193 Numbers of the form 2^k*p^h where k > 0, h >= 0 p is an odd prime.
%F A321193 a(n) = 2 * A070776(n-1) for n > 1. - _Alois P. Heinz_, Nov 20 2018
%e A321193 18 = 2 * 3^2 is in the sequence because it has 1 odd prime factor (3 counts only once).
%e A321193 16 = 2^4 is in the sequence because it has no odd prime factors.
%e A321193 70 = 2 * 5 * 7 is not in the sequence because it has 2 odd prime factors.
%t A321193 n = 0; Table[n = n + 2;
%t A321193 While[Length[FactorInteger[n]] > 2, n = n + 2]; n, {k, 1, 76}]
%o A321193 (PARI) is(n) = n%2==0 && omega(n) <= 2 \\ _Felix Fröhlich_, Nov 01 2018
%o A321193 (PARI) is(n)=my(o=valuation(n,2)); o && isprimepower(n>>o) \\ _Charles R Greathouse IV_, Dec 13 2021
%o A321193 (PARI) list(lim)=my(v=List()); for(k=1,logint(lim\=1,2), listput(v,1<<k)); for(k=1,logint(lim\9,2), my(L=lim>>k); for(e=2,logint(L,3), forprime(p=3, sqrtnint(L,e), listput(v,p^e<<k)))); for(k=1,logint(lim\3,2), forprime(p=3, lim>>k, listput(v,p<<k))); Set(v) \\ _Charles R Greathouse IV_, Dec 13 2021
%Y A321193 Cf. A070776, A100367, A001221, A098902, A100368.
%K A321193 nonn,easy
%O A321193 1,1
%A A321193 _Lei Zhou_, Oct 29 2018