A316147 Numbers, with digits in nondecreasing order, whose product of digits equals the number of digits times the sum of digits.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 36, 44, 159, 167, 235, 333, 1247, 1344, 2226, 11259, 11355, 111279, 111366, 112239, 112246, 112335, 1111377, 1111457, 1112337, 11111388, 11112267, 11113344, 11122236, 11222224, 111111399, 111111559, 111111666, 111112269

Offset

1,3

Comments

This sequence can be used to find terms of A064154 by permuting digits of terms of this sequence.

Links

Table of n, a(n) for n=1..38.

Mathematica

Union@ Flatten@ Reap[ Sow[0]; Do[ If[ FactorInteger[ nd s ][[-1, 1]] <= 7, Sow[ FromDigits /@ Reverse /@ Select[ IntegerPartitions[s, {nd}, Range[9]], Times @@ # == Length[#] Plus @@ # &]]], {nd, 18}, {s, 9 nd}]][[2, 1]] (* terms < 10^18, Giovanni Resta, Jul 18 2018 *)
dnoQ[n_]:=Module[{idn=IntegerDigits[n]}, Min[Differences[idn]]>=0 && Times@@idn==Length[idn]Total[idn]]; Select[Range[0, 111112300], dnoQ] (* Harvey P. Dale, Aug 12 2021 *)

Prog

(PARI) is(n) = my(d = digits(n)); vecsort(d) == d && prod(i=1, #d, d[i]) == #d * vecsum(d) \\ David A. Corneth, Jul 18 2018

Crossrefs

Cf. A064154.

Sequence in context: A343050 A276143 A064154 * A080161 A345405 A257554

Adjacent sequences: A316144 A316145 A316146 * A316148 A316149 A316150

Keyword

nonn,base,easy

Author

David A. Corneth, Jun 25 2018

Status

approved