cp's OEIS Frontend

A334102 Numbers n for which A329697(n) == 2.

%I A334102 #19 Apr 16 2020 18:49:47
%S A334102 7,9,11,13,14,15,18,22,25,26,28,30,36,41,44,50,51,52,56,60,72,82,85,
%T A334102 88,97,100,102,104,112,120,137,144,164,170,176,193,194,200,204,208,
%U A334102 224,240,274,288,289,328,340,352,386,388,400,408,416,448,480,548,576,578,641,656,680,704,769,771,772,776,800,816,832,896,960,1096
%N A334102 Numbers n for which A329697(n) == 2.
%C A334102 Numbers n for which A171462(n) = n-A052126(n) is in A334101.
%C A334102 Numbers k such that A000265(k) is either in A333788 or in A334092.
%C A334102 Each term is either of the form A334092(n)*2^k, for some n >= 1, and k >= 0, or a product of two terms of A334101, whether distinct or not.
%C A334102 Binary weight (A000120) of these terms is always either 2, 3 or 4. It is 2 for those terms that are of the form 9*2^k, 4 for the terms of the form p*q*2^k, where p and q are two distinct Fermat primes (A019434), and 3 for the both terms of the form A334092(n)*2^k, and for the terms of the form (p^2)*(2^k), where p is a Fermat prime > 3.
%o A334102 (PARI)
%o A334102 A000265(n) = (n>>valuation(n,2));
%o A334102 isA019434(n) = ((n>2)&&isprime(n)&&!bitand(n-2,n-1)); \\ Charfun for A019434, Fermat primes.
%o A334102 isA334102(n) = { n = A000265(n); if(isprime(n), isA019434(A000265(n-1)), if(bigomega(n)!=2,0,factorback(apply(isA019434,factor(n)[,1])))); };
%o A334102 (PARI)
%o A334102 A329697(n) = if(!bitand(n,n-1),0,1+A329697(n-(n/vecmax(factor(n)[, 1]))));
%o A334102 isA334102(n) = (2==A329697(n));
%Y A334102 Row 2 of A334100.
%Y A334102 Cf. A000120, A000265, A019434, A052126, A171462, A209229, A329697.
%Y A334102 Cf. A333788 (a subsequence), A334092 (primes present), A334093 (primes that are 1 + some term in this sequence).
%Y A334102 Squares of A334101 form a subsequence of this sequence. Squares of these numbers can be found (as a subset) in A334104, and the cubes in A334106.
%K A334102 nonn
%O A334102 1,1
%A A334102 _Antti Karttunen_, Apr 14 2020