A368215 a(n) is the smallest number k >= 1 that has exactly n divisors in A020487.

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.

Links

Table of n, a(n) for n=1..41.

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

Cf. A000005, A000203, A001157, A020487, A337326.

Sequence in context: A081456 A223403 A263385 * A130279 A030158 A054246

Adjacent sequences: A368212 A368213 A368214 * A368216 A368217 A368218

Keyword

nonn

Author

Marius A. Burtea, Dec 17 2023

Status

approved