A392347 Numbers k such that A000005(k) = A000005(k/d + d) for some d.

2, 4, 8, 14, 15, 20, 21, 26, 32, 33, 34, 38, 44, 45, 52, 56, 57, 62, 69, 74, 75, 85, 86, 93, 94, 98, 99, 104, 106, 116, 118, 122, 128, 129, 133, 134, 135, 136, 140, 141, 142, 145, 147, 148, 152, 158, 164, 166, 171, 175, 176, 177, 178, 189, 196, 201, 202, 205, 207, 213, 214, 217, 218, 224, 226, 230

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

1 is not a term because A000005(1) = 1 < 2 = A000005(1/1 + 1).
2 is a term because A000005(2) = A000005(2/1 + 1) = 2 for d = 1 or d = 2;
4 is a term because A000005(4) = A000005(4/2 + 2) = 3 for only d = 2.

Maple

filter:= proc(n) local t; uses NumberTheory;
  t:= tau(n);
  ormap(d -> tau(n/d+d) = t, Divisors(n))
end proc:
select(filter, [$1..300]); # Robert Israel, Jan 08 2026

Mathematica

Select[Range[230], Sum[Boole[DivisorSigma[0, #]==DivisorSigma[0, #/d+d]], {d, Divisors[#]}]>0 &] (* Stefano Spezia, Jan 08 2026 *)

Prog

(Magma) [k: k in [1..230] | not #[d: d in Divisors(k) | #Divisors(k) eq #Divisors((k div d) + d)] eq 0];
(PARI) isok(k) = #select(x->(x==numdiv(k)), apply(x->numdiv(k/x+x), divisors(k))); \\ Michel Marcus, Jan 08 2026

Crossrefs

Cf. A000005, A161904, A391496.

Superset of A005237.

Sequence in context: A397169 A368490 A076380 * A370840 A049133 A389537

Adjacent sequences: A392344 A392345 A392346 * A392348 A392349 A392350

Keyword

nonn

Author

Juri-Stepan Gerasimov, Jan 07 2026

Status

approved