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

1,2

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

Links

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

Example

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.

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 *)

Prog

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

Crossrefs

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

Sequence in context: A077674 A343742 A357263 * A370688 A357132 A067183

Adjacent sequences: A067074 A067075 A067076 * A067078 A067079 A067080

Keyword

base,nonn

Author

Joseph L. Pe, Feb 18 2002

Extensions

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

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

Status

approved