A337854 a(n) is the smallest number that can be partitioned in exactly n ways as the sum of two Niven numbers.

0, 2, 4, 6, 8, 10, 51, 48, 72, 108, 126, 90, 138, 144, 120, 198, 162, 210, 216, 315, 240, 234, 306, 252, 372, 270, 546, 360, 342, 444, 414, 468, 420, 642, 450, 522, 540, 924, 612, 600, 666, 630, 888, 930, 756, 840, 882, 936, 972, 1098, 1215, 1026, 1212, 1080

Offset

0,2

Links

Table of n, a(n) for n=0..53.

Example

a(0) = 0 because 0 cannot be written as the sum of two Niven numbers.
a(1) = 2 because 2 is uniquely written 2 = 1 + 1, with 1 in A005349.
a(2) = 4 because 4 = 1 + 3 = 2 + 2 and 1, 2, 3 are in A005349.
a(3) = 6 because 6 = 1 + 5 = 2 + 4 = 3 + 3 and 1, 2, 3, 4, 5 are terms in A005349.
a(6) = 51, because 51 = 1 + 50 = 3 + 48 = 6 + 45 = 9 + 42 = 21 + 30 = 24 + 27 and 1, 3, 6, 9, 21, 24, 27, 30, 42, 45, 48, 50 are terms in A005349.

Mathematica

m = 1300; nivens = Select[Range[m], Divisible[#, Plus @@ IntegerDigits[#]] &]; a[n_] := Length[IntegerPartitions[n, {2}, nivens]]; mx = 54; s = Table[-1, {mx}]; c = 0; n = 0; While[c < mx, i = a[n] + 1; If[i <= mx && s[[i]] < 0, c++; s[[i]] = n]; n++]; s (* Amiram Eldar, Sep 27 2020 *)

Prog

(Magma) a:=[]; niven:=func<n|n mod &+Intseq(n) eq 0 >; for n in [0..55] do k:=0; while k le 10000 and #RestrictedPartitions(k, 2, {m:m in [1..k-1]| niven(m)}) ne n do k:=k+1; end  while; Append(~a, k); end for; a;

Crossrefs

Cf. A005349, A337853.

Sequence in context: A134244 A195874 A195873 * A073140 A256342 A171820

Adjacent sequences: A337851 A337852 A337853 * A337855 A337856 A337857

Keyword

nonn,base

Author

Marius A. Burtea, Sep 26 2020

Status

approved