login
A316147
Numbers, with digits in nondecreasing order, whose product of digits equals the number of digits times the sum of digits.
1
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.
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
KEYWORD
nonn,base,easy
AUTHOR
David A. Corneth, Jun 25 2018
STATUS
approved