A305677 - OEIS

%I #26 Mar 25 2024 06:36:02

%S 1,2,8,1,64,256,2048,4,1,131072,262144,32,8388608,33554432,134217728,

%T 1,2147483648,8,34359738368,1024,549755813888,4398046511104,

%U 17592186044416,8192,2,1125899906842624,32,65536,72057594037927936,576460752303423488

%N Number of subsets of {n+1, n+2, ..., A072905(n)-1} whose product has the same squarefree part as n.

%C Conjecture: a(n) > 0.

%C If the conjecture is true, all terms are powers of two, and a(n) >= A259527(n).

%C a(n) = 0 if and only if A066400(n) = 2.

%C a(n) = 0 if and only if A255167(n) = 0.

%C a(n) <= 2^(A067722(n) - 1). - _Peter Kagey_, Nov 13 2018

%H Peter Kagey, <a href="/A305677/b305677.txt">Table of n, a(n) for n = 1..200</a>

%e For n = 3, the a(3) = 8 subsets of {4, 5, ..., 11} with a product with squarefree part of 3 are {4, 5, 6, 9, 10}, {4, 5, 6, 10}, {4, 6, 8}, {4, 6, 8, 9}, {5, 6, 9, 10}, {5, 6, 10}, {6, 8}, and {6, 8, 9}.

%Y Cf. A005117, A006255, A066400, A072905, A255167.

%K nonn

%O 1,2

%A _Peter Kagey_, Jun 08 2018