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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

%I

%S 1,3,8,18,60,150,210,420,390,840,7770,5460,9282,2310,3570,2730,10710,

%T 39270,117810,60060,154770,43890,53130,46410,66990,62790,176358,

%U 106260,30030,642180,1111110,1919190,930930,1688610,1360590,1531530,1291290,570570,1138830,510510,690690,1141140,870870

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

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

%e 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.

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

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

%p m:= nops(D);

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

%p end proc:

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

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

%p for n from 1 while count < N+1 do

%p v:= f(n);

%p if v <= N and V[v]=0 then count:= count+1; V[v]:= n fi

%p od:

%p convert(V,list);

%Y Cf. A340728.

%K nonn

%O 0,2

%A _J. M. Bergot_ and _Robert Israel_, Jan 17 2021

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Last modified April 10 18:04 EDT 2021. Contains 342852 sequences. (Running on oeis4.)