

A305677


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


2



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
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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



