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A368215
a(n) is the smallest number k >= 1 that has exactly n divisors in A020487.
1
1, 4, 16, 36, 256, 100, 200, 576, 400, 800, 2600, 900, 3200, 1800, 16900, 6400, 12800, 3600, 20800, 7200, 11700, 36000, 67600, 14400, 23400, 28800, 32400, 88200, 397800, 64800, 270400, 46800, 152100, 115200, 234000, 93600, 1258400, 230400, 259200, 352800, 1081600
OFFSET
1,2
COMMENTS
a(n) exists for each n because 4^(n-1) has n antiharmonic divisors.
EXAMPLE
a(1) = 1 because 1 has only one divisor 1 = A020487(1).
The numbers 2 and 3 have only the divisor 1 in A020487 and 4 has the divisors 1 = A020487(1) and 4 = A020487(2), so a(2) = 4.
MATHEMATICA
f[n_] := DivisorSum[n, 1 &, Divisible[DivisorSigma[2, #], DivisorSigma[1, #]] &]; seq[len_] := Module[{s = Table[0, {len}], c = 0, n = 1}, While[c < len, If[(i = f[n]) <= len && s[[i]] == 0, c++; s[[i]] = n]; n++]; s]; seq[25] (* Amiram Eldar, Dec 18 2023 *)
PROG
(Magma) f:=func<n|DivisorSigma(2, n) mod DivisorSigma(1, n) eq 0>; a:=[]; for n in [1..41] do k:=1; while #[d:d in Divisors(k)|f(d)] ne n do k:=k+1; end while; Append(~a, k); end for; a;
(PARI) a(n) = my(k=1); while(sumdiv(k, d, sigma(d, 2)%sigma(d)==0) != n, k++); k; \\ Michel Marcus, Dec 18 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Marius A. Burtea, Dec 17 2023
STATUS
approved