A222639 Square root of the square part of the total number of arrangements of a set with n elements.

1, 1, 1, 4, 1, 1, 1, 10, 1, 1, 1, 2, 13, 1, 1, 2, 1, 1, 1, 20, 1, 1, 1, 58, 1, 1, 1, 2, 1, 1, 1, 2, 5, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 2, 5, 1, 1, 2, 1, 1, 1, 8, 1, 1, 1, 2, 1, 5, 1, 2, 1, 1, 1, 2, 23, 1, 1, 4, 1, 5, 1, 2, 1, 37

Offset

0,4

Links

Table of n, a(n) for n=0..73.

F. Luca and I. E. Shparlinski, On the squarefree parts of floor(e*n!), Glasgow Math. J., 49 (2007), 391-403.

Formula

a(n) = sqrt(A000522(n)/core(A000522(n))).

Prog

(PARI) a(n) = core(n! * polcoeff(exp(x + x*O(x^n)) / (1 - x), n), 1)[2]

Crossrefs

Cf. A000188, A000522, A007913, A222637.

Sequence in context: A112538 A008477 A303278 * A184729 A127707 A113196

Adjacent sequences: A222636 A222637 A222638 * A222640 A222641 A222642

Keyword

nonn

Author

Michel Marcus, Feb 27 2013

Status

approved