A065774 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.

2, 3, 4, 5, 7, 18, 25, 154, 329, 418, 442, 532, 1519, 1826, 2354, 2472, 2781, 3383, 4343, 4712, 5282, 5561, 6171, 6623, 7922, 9331, 9911, 11248, 12328, 12773, 13125, 14193, 15194, 16512, 17267, 19852, 21479, 24516, 26522, 31816, 32661, 36512

Offset: 1

Author

Jason Earls, Dec 04 2001

Keywords

• base
• easy
• nonn

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 400 terms from Harry J. Smith)

Crossrefs

Cf. A067173, A001414, A007954.

Programs

Mathematica

Select[Range[2, 10^5], Times @@ IntegerDigits @ # == Plus @@ Times @@@ FactorInteger @ # &] (* Giovanni Resta, Apr 23 2017 *)

PARI

ProdD(x)= { local(p=1); while (x>9 && p>0, p*=(x-10*(x\10)); x\=10); return(p*x) }
sopfr(n)= { local(f,s=0); f=factor(n); for(i=1, matsize(f)[1], s+=f[i, 1]*f[i, 2]); return(s) }
{ 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

Extensions

Offset changed from 0 to 1 by Harry J. Smith, Oct 30 2009