OFFSET
1,2
COMMENTS
a(n) is the greedy inverse of A336041: the smallest number with exactly n divisors d such that d / tau(d) is also an integer.
Numbers 1 and 2 are only numbers m such that d / tau(d) is an integer for all divisors d of m.
FORMULA
a(n) = min{ k: A336041(k)=n}. - R. J. Mathar, Nov 24 2020
EXAMPLE
a(3) = 8 because 8 with divisors 1, 2, 4 and 8 is the smallest number with 3 refactorable divisors: 1 / tau(1) = 1, 2 / tau(2) = 1, 8 / tau(8) = 2.
MATHEMATICA
f[n_] := DivisorSum[n, 1 &, Divisible[#, DivisorSigma[0, #]] &]; m = 43; s = Table[0, {m}]; c = 0; n = 1; While[c < m, i = f[n]; If[i <= m && s[[i]] == 0, c++; s[[i]] = n]; n++]; s (* Amiram Eldar, Oct 24 2020 *)
PROG
(Magma) [Min([m: m in[1..10^5] | #[d: d in Divisors(m) | IsIntegral(d / #Divisors(d))] eq n]): n in [1..12]]
CROSSREFS
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Oct 24 2020
STATUS
approved