A067173 Numbers n such that the sum of the prime factors of n equals the product of the digits of n.

2, 3, 5, 7, 126, 154, 315, 329, 342, 418, 442, 1134, 1826, 2354, 3383, 4343, 5282, 5561, 6623, 7515, 7922, 9331, 9911, 12773, 13344, 14161, 15194, 17267, 18292, 21479, 22831, 26216, 26522, 29812, 32129, 33128, 33912, 57721, 81191, 81524

Offset

1,1

Links

Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 184 terms from Harvey P. Dale)

Example

The prime factors of 315 are 3,5,7, which sum to 15, the product of the digits of 315, so 315 is a term of the sequence.

Mathematica

f[n_] := Module[{a, l, t, r}, a = FactorInteger[n]; l = Length[a]; t = Table[a[[i]][[1]], {i, 1, l}]; r = Sum[t[[i]], {i, 1, l}]]; g[n_] := Module[{b, m, s}, b = IntegerDigits[n]; m = Length[b]; s = Product[b[[i]], {i, 1, m}]]; Select[Range[10^5], f[ # ] == g[ # ] &]
Select[Range[2, 100000], Total[FactorInteger[#][[All, 1]]] == Times@@ IntegerDigits[ #]&] (* Harvey P. Dale, Feb 15 2017 *)

Crossrefs

Cf. A065774, A006753.

Sequence in context: A076609 A117059 A117058 * A357262 A340113 A090718

Adjacent sequences: A067170 A067171 A067172 * A067174 A067175 A067176

Keyword

base,nonn

Author

Joseph L. Pe, Feb 18 2002

Status

approved