1,2

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

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

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.

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

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

Sequence in context: A077674 A343742 A357263 * A389195 A370688 A357132

Adjacent sequences: A067074 A067075 A067076 * A067078 A067079 A067080

base,nonn

Joseph L. Pe, Feb 18 2002

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

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

approved