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

Author

Joseph L. Pe, Feb 18 2002

Keywords

• base
• nonn

Examples

			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.
		

Links

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

Crossrefs

Cf. A065774, A006753.

Programs

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 *)