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A369383
The smallest number k that can be partitioned in n ways as the sum of two numbers from A003601.
0
1, 2, 6, 12, 18, 20, 26, 28, 38, 34, 42, 48, 44, 50, 52, 58, 62, 60, 68, 80, 74, 76, 88, 84, 92, 129, 98, 110, 100, 114, 108, 122, 134, 116, 144, 132, 171, 138, 140, 146, 148, 160, 174, 162, 182, 156, 170, 172, 184, 198, 200, 180, 206, 188, 257, 253, 196, 204
OFFSET
0,2
EXAMPLE
a(0) = 1 because 1 cannot be written as the sum of two terms in A003601.
2 = 1 + 1 = A003601(1) + A003601(1), so a(1) = 2.
The numbers 3 and 5 cannot be written as the sum of two terms in A003601, and 4 = 1 + 3 = A003601(1) + A003601(2) is the only writing with terms in A003601. The number 6 can be written 6 = 1 + 5 = A003601(1) + A003601(3) and 6 = 3 + 3 = A003601(2) + A003601(2), so a(2) = 6.
PROG
(Magma) f:=func<n|DivisorSigma(1, n) mod DivisorSigma(0, n) eq 0>; b:=[k: k in [1..1000] |f(n)]; a:=[]; for n in [0..60] do k:=1; while #RestrictedPartitions(k, 2, Set(b)) ne n do k:=k+1; end while; Append(~a, k); end for; a;
CROSSREFS
KEYWORD
nonn
AUTHOR
Marius A. Burtea, Jan 25 2024
STATUS
approved