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 A067173 Numbers n such that the sum of the prime factors of n equals the product of the digits of n. 3

%I

%S 2,3,5,7,126,154,315,329,342,418,442,1134,1826,2354,3383,4343,5282,

%T 5561,6623,7515,7922,9331,9911,12773,13344,14161,15194,17267,18292,

%U 21479,22831,26216,26522,29812,32129,33128,33912,57721,81191,81524

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

%H Giovanni Resta, <a href="/A067173/b067173.txt">Table of n, a(n) for n = 1..10000</a> (first 184 terms from Harvey P. Dale)

%e 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.

%t 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[ # ] &]

%t Select[Range[2,100000],Total[FactorInteger[#][[All,1]]] == Times@@ IntegerDigits[ #]&] (* _Harvey P. Dale_, Feb 15 2017 *)

%Y Cf. A065774, A006753.

%K base,nonn

%O 1,1

%A _Joseph L. Pe_, Feb 18 2002

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Last modified January 27 06:18 EST 2022. Contains 350601 sequences. (Running on oeis4.)