A359750 Numbers that are a product of one or more factorials j!, j >= 2, in at least two ways.

24, 48, 96, 144, 192, 288, 384, 576, 720, 768, 864, 1152, 1440, 1536, 1728, 2304, 2880, 3072, 3456, 4320, 4608, 5184, 5760, 6144, 6912, 8640, 9216, 10368, 11520, 12288, 13824, 17280, 18432, 20736, 23040, 24576, 25920, 27648, 31104, 34560, 36864, 40320, 41472, 46080

Offset

1,1

Links

Table of n, a(n) for n=1..44.

Example

24 = 2! * 3! = 4!.
144 = (2!)^2 * (3!)^2 = 3! * 4!.

Prog

(PARI) is(n) = { if(n == 1, return(0)); my(i, factorials, e, res, v); f = factor(n); if(prime(#f~) != f[#f~, 1], return(0); ); if(f[, 2] != vecsort(f[, 2], , 4), return(0); ); factorials = List(); e = List(); res = List(); for(i = 2, oo, v = valuation(n, i!); if(v > 0, listput(factorials, i!); listput(e, v); , break ) ); forvec(x = vector(#e-1, i, [0, e[i+1]]), c = prod(i = 1, #e-1, factorials[i+1]^x[i]); if(c <= n && denominator(n/c) == 1&& 1 << logint(n/c, 2) == n/c, listput(res, concat([valuation(n/c, 2)], x)) ) ); #res >= 2 } \\ David A. Corneth, Jan 13 2023

Crossrefs

Cf. A001013.

Sequence in context: A083541 A230761 A073763 * A292834 A362941 A030021

Adjacent sequences: A359747 A359748 A359749 * A359751 A359752 A359753

Keyword

nonn

Author

David A. Corneth, Jan 13 2023

Status

approved