A337853 a(n) is the number of partitions of n as the sum of two Niven numbers.

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

Rémy Sigrist, Table of n, a(n) for n = 0..10000

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]];

Crossrefs

Cf. A005349, A116357, A172151, A172398, A180149, A280829, A319468, A302479, A319395, A337854.

Sequence in context: A341721 A290323 A260254 * A282711 A035100 A303594

Adjacent sequences: A337850 A337851 A337852 * A337854 A337855 A337856

Keyword

nonn,base

Author

Marius A. Burtea, Sep 26 2020

Status

approved