

A067173


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


3



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
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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 * A340113 A090718 A167853
Adjacent sequences: A067170 A067171 A067172 * A067174 A067175 A067176


KEYWORD

base,nonn


AUTHOR

Joseph L. Pe, Feb 18 2002


STATUS

approved



