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A067077 Numbers whose product of distinct prime factors is equal to its sum of digits.

%I A067077 #21 Dec 05 2024 14:46:03
%S A067077 1,2,3,5,6,7,24,375,392,640,2401,4802,4913,6400,7744,17576,42592,
%T A067077 64000,106496,234256,295936,468750,546875,628864,640000,877952,
%U A067077 1124864,1966080,2839714,3687936,4687500,4816896,4952198,6400000,6453888
%N A067077 Numbers whose product of distinct prime factors is equal to its sum of digits.
%C A067077 The product of the distinct prime factors of n (the squarefree kernel of n) is also denoted by rad(n) = A007947(n). - _Giovanni Resta_, Apr 21 2017
%H A067077 Giovanni Resta, <a href="/A067077/b067077.txt">Table of n, a(n) for n = 1..10000</a> (first 71 terms from Harry J. Smith)
%e A067077 The prime factors of 375 are 3,5, which have product = 15, the sum of the digits of 375, so 375 is a term of the sequence.
%t A067077 f[n_] := Times@@ (First/@ FactorInteger[n]); g[n_] := Plus @@ IntegerDigits[n]; Select[Range[10^5], f[#] == g[#] &] (* or *)
%t A067077 nd=12; up=10^nd; L={1}; Do[If[SquareFreeQ[su], ps = First /@ FactorInteger[su]; nps = Length@ ps; Clear[ric]; ric[n_, i_] := Block[{e = 0, m}, If[i > nps, If[Plus @@ IntegerDigits[su n] == su, Sow[su n]], While[ (m = n ps[[i]]^e ) su < up, ric[m, i+1]; e++]]]; z = Reap[ ric[1, 1]][[2]]; If[z != {}, L = Union[L, z[[1]]]]], {su, 2, 9 nd}]; L (* fast, terms < 10^12, _Giovanni Resta_, Apr 21 2017 *)
%t A067077 Select[Range[65*10^5],Times@@FactorInteger[#][[All,1]]==Total[ IntegerDigits[ #]]&] (* _Harvey P. Dale_, Dec 16 2018 *)
%o A067077 (PARI) isok(k)={vecprod(factor(k)[,1]) == sumdigits(k)} \\ _Harry J. Smith_, May 06 2010
%Y A067077 Cf. A007947, A006753, A057531, A057532, A050689, A070274, A070275, A063737, A285494.
%K A067077 base,nonn
%O A067077 1,2
%A A067077 _Joseph L. Pe_, Feb 18 2002
%E A067077 a(19)-a(35) from _Donovan Johnson_, Sep 29 2009
%E A067077 a(1)=1 prepended by _Giovanni Resta_, Apr 21 2017