login
A359750
Numbers that are a product of one or more factorials j!, j >= 2, in at least two ways.
1
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
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
KEYWORD
nonn
AUTHOR
David A. Corneth, Jan 13 2023
STATUS
approved