A305677 Number of subsets of {n+1, n+2, ..., A072905(n)-1} whose product has the same squarefree part as n.

1, 2, 8, 1, 64, 256, 2048, 4, 1, 131072, 262144, 32, 8388608, 33554432, 134217728, 1, 2147483648, 8, 34359738368, 1024, 549755813888, 4398046511104, 17592186044416, 8192, 2, 1125899906842624, 32, 65536, 72057594037927936, 576460752303423488

Offset: 1

Author

Peter Kagey, Jun 08 2018

Keywords

• nonn

Comments

Conjecture: a(n) > 0.

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

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

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

a(n) <= 2^(A067722(n) - 1). - Peter Kagey, Nov 13 2018

Examples

			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}.
		

Links

• Peter Kagey, Table of n, a(n) for n = 1..200

Crossrefs

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