A070274 Numbers n such that sum of digits of n equals the squarefree part of n.

1, 2, 3, 5, 6, 7, 12, 24, 100, 150, 200, 300, 320, 375, 500, 600, 640, 700, 704, 735, 832, 960, 1014, 1088, 1200, 1815, 2023, 2400, 2535, 2940, 3549, 3610, 3840, 4046, 4335, 4913, 5054, 5376, 5415, 5491, 6069, 6137, 6358, 6647, 7260, 7581, 7942, 8959, 9386

Offset: 1

Author

Benoit Cloitre, May 09 2002

Keywords

• nonn
• base

Comments

The squarefree part of x, core(x), is the smallest integer such that x*core(x) is a square.

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007913, A057531, A057532, A050689, A070275, A063737, A067077, A285494.

Programs

Mathematica

core[n_]:=Block[{f=FactorInteger[n], p, e}, {p, e} = Transpose[f]; Times@@ (p^Mod[e, 2])]; Select[Range[10^4], core[#] == Plus @@ IntegerDigits[#] &] (* Giovanni Resta, Apr 21 2017 *)

PARI

list(lim)=my(v=List()); forfactored(n=1,lim\1, if(core(n)==sumdigits(n[1]), listput(v,n[1]))); Vec(v) \\ Charles R Greathouse IV, Nov 05 2017

Extensions

Data corrected by Giovanni Resta, Apr 21 2017