A065774 - OEIS

%I #22 Apr 13 2024 14:57:30

%S 2,3,4,5,7,18,25,154,329,418,442,532,1519,1826,2354,2472,2781,3383,

%T 4343,4712,5282,5561,6171,6623,7922,9331,9911,11248,12328,12773,13125,

%U 14193,15194,16512,17267,19852,21479,24516,26522,31816,32661,36512

%N Numbers k such that the product of the digits of k is equal to the sum of the prime factors of k, counted with multiplicity.

%H Giovanni Resta, <a href="/A065774/b065774.txt">Table of n, a(n) for n = 1..10000</a> (first 400 terms from Harry J. Smith)

%t Select[Range[2, 10^5], Times @@ IntegerDigits @ # == Plus @@ Times @@@ FactorInteger @ # &] (* _Giovanni Resta_, Apr 23 2017 *)

%o (PARI) ProdD(x)= { local(p=1); while (x>9 && p>0, p*=(x-10*(x\10)); x\=10); return(p*x) }

%o sopfr(n)= { local(f,s=0); f=factor(n); for(i=1, matsize(f)[1], s+=f[i, 1]*f[i, 2]); return(s) }

%o { n=0; for (m=1, 10^9, if (ProdD(m) == sopfr(m), write("b065774.txt", n++, " ", m); if (n==400, return)) ) } \\ _Harry J. Smith_, Oct 30 2009

%Y Cf. A067173, A001414, A007954.

%K base,easy,nonn

%O 1,1

%A _Jason Earls_, Dec 04 2001

%E Offset changed from 0 to 1 by _Harry J. Smith_, Oct 30 2009