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
Keywords
Examples
a(3) = 18 has 3 such divisors: 2+1=3, 5+1=6, 17+1=18, and is the least number with exactly 3.
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.
Programs
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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 *) -
PARI
a(n) = my(k=1); while (sumdiv(k, d, isprime(d-1)) != n, k++); k; \\ Michel Marcus, Feb 05 2021
Comments