OFFSET
0,2
COMMENTS
All deficient numbers k > 1 (A005100) have only one subset, {1, k}, whose sum is k+1.
LINKS
Robert G. Wilson v, Table of n, a(n) for n = 0..262
EXAMPLE
a(0) = 1 since there exists no subset of the divisors of 1 which sum to 2.
a(1) = 2. 2 is the least deficient number greater than 1.
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.
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.
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.
MAPLE
f:= proc(n) local x, d; coeff(expand(mul(1+x^d, d=numtheory:-divisors(n))), x, n+1) end proc:
N:= 60: # 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 V[v]:= n; count:= count+1 fi
od:
convert(V, list); # Robert Israel, Jan 14 2023
MATHEMATICA
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]
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, Dec 19 2022
STATUS
approved