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

1,2

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

Links

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

Example

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}.

Crossrefs

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

Sequence in context: A062038 A318106 A308036 * A296569 A021082 A029672

Adjacent sequences: A305674 A305675 A305676 * A305678 A305679 A305680

Keyword

nonn

Author

Peter Kagey, Jun 08 2018

Status

approved