A389254 Smallest k for which the number of divisors d of k such that A000005(d*k) = A000005(k + d) is equal to n, or -1 if no such k exists.

1, 4, 2, 98, 1269, 8019, 149144, 2144779, 17271711, 5403125

Offset

0,2

Comments

a(n) has at least n divisors. - David A. Corneth, Jan 12 2026

Links

Table of n, a(n) for n=0..9.

Mathematica

seq[len_] := Module[{v = Table[0, {len}], k = 1, c = 0, i}, While[c < len, i = DivisorSum[k, 1 &, DivisorSigma[0, #*k] == DivisorSigma[0, k + #] &] + 1; If[i <= len && v[[i]] == 0, c++; v[[i]] = k]; k++]; v]; seq[7] (* Amiram Eldar, Jan 12 2026 *)

Prog

(Magma) [Min([k: k in [1..10^4] | #[d: d in Divisors(k) | #Divisors(d*k) eq #Divisors(k + d)] eq n]): n in [0..5]];
(PARI) isok(k, n) = sumdiv(k, d, numdiv(k*d)==numdiv(k+d)) == n;
a(n) = my(k=1); while(!isok(k, n), k++); k; \\ Michel Marcus, Jan 12 2026

Crossrefs

Cf. A000005.

Sequence in context: A236381 A384941 A335300 * A201228 A010319 A266069

Adjacent sequences: A389251 A389252 A389253 * A389255 A389256 A389257

Keyword

nonn,more

Author

Juri-Stepan Gerasimov, Jan 11 2026

Extensions

a(7)-a(9) from Amiram Eldar, Jan 12 2026

Status

approved