A131387 Product of the nonzero digital products of n for all the bases 1 to n (a 'total digital-product factorial').

1, 1, 1, 1, 2, 4, 12, 48, 48, 192, 2880, 2880, 25920, 552960, 3265920, 1935360, 116121600, 278691840, 9405849600, 26754416640, 94058496000, 3210529996800, 869100503040000, 423789959577600, 927040536576000, 135612787064832000

Offset: 1

Author

Hieronymus Fischer, Jul 08 2007

Keywords

• nonn
• base

Programs

PARI

a(n) = {p = 1; for (b=2, n, digs = digits(n, b); p *= prod(k=1, #digs, if (digs[k], digs[k], 1));); return (p);} \\ Michel Marcus, Jul 15 2013

Formula

a(n)=product{1<=p<=n, dp_p(n)} where dp_p(n) = product of the nonzero digits of n in base p.

Cf. A131385, A010786, A007954.