A392895 - OEIS

%I #30 Feb 06 2026 16:30:20

%S 1,2,4,8,16,6,64,45,20,105,70,12,135,1377,225,42,1450,40,988,30,819,

%T 825,24,348,2541,765,525,112,495,162,7144,675,36,294,6669,306,315,

%U 3645,5750,364,342,204,48,1472,2500,1464,220,3618,1216,3560,228,224,1088,3910,2130,150,3410,1936

%N Least number k for which there exist exactly n subsets of divisors of k such that k is divisible by their sum.

%H Sean A. Irvine, <a href="/A392895/b392895.txt">Table of n, a(n) for n = 1..632</a> (terms 1..300 from Michael S. Branicky)

%e 6 is the least number for which there exist exactly 6 subsets of divisors of 6: [[1], [2], [3], [6], [1, 2], [1, 2, 3]] such that 6 is respectively divisible by their sums [1, 2, 3, 6, 3, 6].

%e 45 is the least number for which there exist exactly 8 subsets of divisors of 45: [[1], [3], [5], [9], [15], [45], [1, 3, 5], [1, 5, 9]] such that 45 is respectively divisible by their sums [1, 3, 5, 9, 15, 45, 9, 15].

%o (PARI) isok(k, n) = my(d = divisors(k), nb=0); forsubset(#d, s, if (#s && !(k % sum(i=1,#s,d[s[i]])), nb++; if (nb>n, return(0)))); nb==n;

%o a(n) = my(k=1); while (!isok(k,n), k++); k; \\ _Michel Marcus_, Jan 26 2026

%o (Python)

%o from itertools import chain, combinations, count, islice

%o from sympy import divisors

%o def powerset(s): # skipping empty set

%o     return chain.from_iterable(combinations(s, r) for r in range(1, len(s)+1))

%o def a(n):

%o     for k in count(1):

%o         divs = divisors(k)

%o         if 2**len(divs) - 1 < n: continue

%o         c = 1 # count {k}

%o         for s in powerset(divs[:-1]):

%o             if k%sum(s) == 0: c += 1

%o             if c > n: break

%o         if c == n: return k

%o print([a(n) for n in range(1, 31)]) # _Michael S. Branicky_, Jan 28 2026

%Y Cf. A096356, A065218, A392652.

%K nonn,nice

%O 1,2

%A _Jean-Marc Rebert_, Jan 26 2026

%E More terms from _Michel Marcus_, Jan 26 2026