cp's OEIS Frontend

A359197 Least number k having n subsets of its divisors whose sum is k+1.

%I A359197 #41 Mar 24 2025 06:45:57
%S A359197 1,2,18,12,162,24,342,80,36,198,156,48,126,150,1430,132,1110,1302,
%T A359197 1672,448,90,96,784,1190,1408,84,320,72,1064,3100,16048,744,702,60,
%U A359197 920,690,984,750,594,2300,714,696,11024,192,11696,400,2028,680,728,1548,10672,546,616,2156,462,324,37888,510,4698
%N A359197 Least number k having n subsets of its divisors whose sum is k+1.
%C A359197 All deficient numbers k > 1 (A005100) have only one subset, {1, k}, whose sum is k+1.
%H A359197 Robert G. Wilson v, <a href="/A359197/b359197.txt">Table of n, a(n) for n = 0..262</a>
%e A359197 a(0) = 1 since there exists no subset of the divisors of 1 which sum to 2.
%e A359197 a(1) = 2. 2 is the least deficient number greater than 1.
%e A359197 a(2) = 18 since two subsets of its divisors, {1, 18} and {1, 3, 6, 9}, sum to 19, and no smaller number has this property.
%e A359197 a(3) = 12 since three subsets of its divisors, {1, 12}, {3, 4, 6} and {1, 2, 4, 6}, sum to 13, and no smaller number has this property.
%e A359197 a(4) = 162 since {1, 162}, {1, 27, 54, 81}, {1, 9, 18, 54, 81} and {1, 3, 6, 18, 54, 81} sum to 163, and no smaller number has this property.
%p A359197 f:= proc(n) local x,d; coeff(expand(mul(1+x^d, d=numtheory:-divisors(n))),x,n+1) end proc:
%p A359197 N:= 60: # for a(0)..a(N)
%p A359197 V:= Array(0..N): count:= 0:
%p A359197 for n from 1 while count < N+1 do
%p A359197   v:= f(n);
%p A359197 if v <= N and V[v] = 0 then V[v]:= n; count:= count+1 fi
%p A359197 od:
%p A359197 convert(V,list); # _Robert Israel_, Jan 14 2023
%t A359197 f[n_] := Block[{d = Divisors@ n}, SeriesCoefficient[ Series[ Product[1 + x^d[[i]], {i, Length@ d}], {x, 0, n +1}], n +1]]; j = 1; t[_] := 0; While[ j < 10001, b = f@j; If[ t[b] == 0, t[b] = j]; j++]; t /@ Range[0, 50]
%Y A359197 Cf. A005100, A359196.
%K A359197 nonn,look
%O A359197 0,2
%A A359197 _Robert G. Wilson v_, Dec 19 2022