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

Author

Michel Marcus, Feb 27 2013

Keywords

• nonn

Links

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

Crossrefs

Cf. A000188, A000522, A007913, A222637.

Programs

PARI

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

Formula

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