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

1, 2, 3, 5, 6, 7, 24, 375, 392, 640, 2401, 4802, 4913, 6400, 7744, 17576, 42592, 64000, 106496, 234256, 295936, 468750, 546875, 628864, 640000, 877952, 1124864, 1966080, 2839714, 3687936, 4687500, 4816896, 4952198, 6400000, 6453888

Offset: 1

Author

Joseph L. Pe, Feb 18 2002

Keywords

• base
• nonn

Comments

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

Examples

			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.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 71 terms from Harry J. Smith)

Crossrefs

Cf. A007947, A006753, A057531, A057532, A050689, A070274, A070275, A063737, A285494.

Programs

Mathematica

f[n_] := Times@@ (First/@ FactorInteger[n]); g[n_] := Plus @@ IntegerDigits[n]; Select[Range[10^5], f[#] == g[#] &] (* or *)
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 *)
Select[Range[65*10^5],Times@@FactorInteger[#][[All,1]]==Total[ IntegerDigits[ #]]&] (* Harvey P. Dale, Dec 16 2018 *)

PARI

isok(k)={vecprod(factor(k)[,1]) == sumdigits(k)} \\ Harry J. Smith, May 06 2010

Extensions

a(19)-a(35) from Donovan Johnson, Sep 29 2009

a(1)=1 prepended by Giovanni Resta, Apr 21 2017