A341119 a(n) is the least positive number that has exactly n divisors d such that d-1 is prime.

1, 3, 6, 18, 12, 36, 24, 48, 72, 120, 168, 336, 240, 540, 360, 960, 840, 1080, 720, 1680, 3024, 1440, 2160, 2880, 2520, 6480, 4320, 14040, 8640, 5040, 9240, 7560, 23520, 12600, 18480, 10080, 33600, 22680, 15120, 20160, 36960, 27720, 47880, 40320, 37800, 47520, 30240, 80640, 85680, 65520, 60480

Offset

0,2

Comments

a(n) is the least positive solution to A072627(k) = n.

The conjectured terms are exact if for 0 <= n <= 10000 we have a(n) / A046523(A000005(a(n))) <= 9. For the found terms, a(n) / A046523(A000005(a(n))) <= 7.3. - David A. Corneth, Jun 15 2022

Links

Robert G. Wilson v, Table of n, a(n) for n = 0..1740 (first 216 terms from Robert Israel)

David A. Corneth, Conjectured first 10001 terms.

Example

a(3) = 18 has 3 such divisors: 2+1=3, 5+1=6, 17+1=18, and is the least number with exactly 3.

Maple

f:= proc(n) nops(select(t -> isprime(t-1), numtheory:-divisors(n))) end proc:
N:= 60: count:= 0:
V:= Array(0..N):
for n from 1 while count < N+1 do
  v:= f(n);
  if v <= N and V[v] = 0 then
    count:=count+1;
    V[v]:= n;
  fi;
od:
convert(V, list);

Mathematica

With[{s = Array[DivisorSum[#, 1 &, PrimeQ[# - 1] &] &, 10^5]}, Array[FirstPosition[s, #][[1]] &, 51, 0]] (* Michael De Vlieger, Feb 05 2021 *)

Prog

(PARI) a(n) = my(k=1); while (sumdiv(k, d, isprime(d-1)) != n, k++); k; \\ Michel Marcus, Feb 05 2021

Crossrefs

Cf. A000005, A008864, A046523, A067846, A072627, A341099.

Sequence in context: A274103 A195995 A248324 * A078318 A193433 A074370

Adjacent sequences: A341116 A341117 A341118 * A341120 A341121 A341122

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Feb 05 2021

Status

approved