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A337853
a(n) is the number of partitions of n as the sum of two Niven numbers.
3
0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 5, 5, 5, 4, 4, 3, 3, 3, 3, 3, 4, 3, 4, 4, 4, 4, 5, 4, 5, 4, 4, 4, 3, 2, 4, 3, 3, 4, 3, 3, 5, 3, 4, 5, 4, 4, 7, 4, 5, 6, 5, 3, 7, 4, 4, 6, 4, 2, 7, 3, 4, 5, 4, 3, 7, 3, 4, 5, 4, 3, 8, 3, 4, 6, 3, 3, 6, 2, 5, 6, 5, 3, 8, 4, 4, 6
OFFSET
0,5
COMMENTS
a(n) >= 1 for n >= 2 ?.
For n <= 200000, a(n) = 1 only for n = 2, 3, 299, (2 = 1 + 1, 3 = 1 + 2, 299 = 1 + 288) and a(n) = 2 only for n in {4, 5, 35, 59, 79, 95, 97, 149, 169, 179, 389}.
LINKS
EXAMPLE
0 and 1 cannot be decomposed as the sum of two Niven numbers, so a(0) = a(1) = 0.
4 = 1 + 3 = 2 + 2 and 1, 2, 3 are in A005349, so a(4) = 2.
15 = 3 + 12 = 5 + 10 = 6 + 9 = 7 + 8 and 3, 5, 6, 7, 8, 9, 10, 12 are in A005349, so a(15) = 4.
MATHEMATICA
m = 100; nivens = Select[Range[m], Divisible[#, Plus @@ IntegerDigits[#]] &]; a[n_] := Length[IntegerPartitions[n, {2}, nivens]]; Array[a, m, 0] (* Amiram Eldar, Sep 27 2020 *)
PROG
(Magma) niven:=func<n | n mod &+Intseq(n) eq 0>; [#RestrictedPartitions(n, 2, {k: k in [1..n-1] | niven(k)}): n in [0..100]];
KEYWORD
nonn,base
AUTHOR
Marius A. Burtea, Sep 26 2020
STATUS
approved