OFFSET
1,4
COMMENTS
a(1) = 1 (an empty product).
LINKS
FORMULA
EXAMPLE
For n = 36 = 2^2 * 3^2 the combinations of the exponents are [], [2] (as exponent of 2), [2] (as exponent of 3) and [2, 2]. Taking products of these multisets we get 1 (as an empty product), 2, 2 and 4. Thus a(36) = 1! * 2! * 2! * 4! = 1*2*2*24 = 96.
For n = 72 = 2^3 * 3^2 the combinations of the exponents are [], [2], [3] and [2, 3]. Taking products of these multisets we get 1, 2, 3 and 6. Thus a(72) = 1! * 2! * 3! * 6! = 1*2*6*720 = 8640.
MATHEMATICA
Array[Apply[Times, Map[Times @@ # &, Subsets@ FactorInteger[#][[All, -1]]]!] &, 105] (* Michael De Vlieger, Oct 23 2017 *)
PROG
(PARI)
A293902(n) = { my(exp_combos=powerset(factor(n)[, 2]), m=1); for(i=1, #exp_combos, m *= vecproduct(exp_combos[i])!); m; };
vecproduct(v) = { my(m=1); for(i=1, #v, m *= v[i]); m; };
powerset(v) = { my(siz=2^length(v), pv=vector(siz)); for(i=0, siz-1, pv[i+1] = choosebybits(v, i)); pv; };
choosebybits(v, m) = { my(s=vector(hammingweight(m)), i=j=1); while(m>0, if(m%2, s[j] = v[i]; j++); i++; m >>= 1); s; };
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 22 2017
STATUS
approved