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

7, 9, 11, 13, 14, 15, 18, 22, 25, 26, 28, 30, 36, 41, 44, 50, 51, 52, 56, 60, 72, 82, 85, 88, 97, 100, 102, 104, 112, 120, 137, 144, 164, 170, 176, 193, 194, 200, 204, 208, 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

Offset: 1

Author

Antti Karttunen, Apr 14 2020

Keywords

• nonn

Comments

Numbers n for which A171462(n) = n-A052126(n) is in A334101.

Numbers k such that A000265(k) is either in A333788 or in A334092.

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.

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.

Crossrefs

Row 2 of A334100.

Cf. A000120, A000265, A019434, A052126, A171462, A209229, A329697.

Cf. A333788 (a subsequence), A334092 (primes present), A334093 (primes that are 1 + some term in this sequence).

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.

Programs

PARI

A000265(n) = (n>>valuation(n,2));
isA019434(n) = ((n>2)&&isprime(n)&&!bitand(n-2,n-1)); \\ Charfun for A019434, Fermat primes.
isA334102(n) = { n = A000265(n); if(isprime(n), isA019434(A000265(n-1)), if(bigomega(n)!=2,0,factorback(apply(isA019434,factor(n)[,1])))); };

PARI

A329697(n) = if(!bitand(n,n-1),0,1+A329697(n-(n/vecmax(factor(n)[, 1]))));
isA334102(n) = (2==A329697(n));