A340729 - OEIS

A340729

a(n) is the least k such that there are exactly n divisors d of k for which k/d-d is prime.

1, 3, 8, 18, 60, 150, 210, 420, 390, 840, 7770, 5460, 9282, 2310, 3570, 2730, 10710, 39270, 117810, 60060, 154770, 43890, 53130, 46410, 66990, 62790, 176358, 106260, 30030, 642180, 1111110, 1919190, 930930, 1688610, 1360590, 1531530, 1291290, 570570, 1138830, 510510, 690690, 1141140, 870870

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OFFSET

0,2

COMMENTS

a(n) is the least solution of A340728(k) = n.

LINKS

Table of n, a(n) for n=0..42.

EXAMPLE

a(3) = 18 because there are 3 such divisors of 18, namely 1,2,3: 18/1-1 = 17, 18/2-2 = 7 and 18/3-3 = 3, and 18 is the least number with 3 such divisors.

MAPLE

f:= proc(n) local D, i, m;

D:= sort(convert(numtheory:-divisors(n), list));

m:= nops(D);

nops(select(i -> isprime(D[m+1-i]-D[i]), [$1..(m+1)/2]));

end proc:

N:= 30: # for a(0)..a(N)

V:= Array(0..N): count:= 0:

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: