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

1,2

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A039058 A362454 A046158 * A088968 A328451 A057924

Adjacent sequences: A070271 A070272 A070273 * A070275 A070276 A070277

Keyword

nonn,base

Author

Benoit Cloitre, May 09 2002

Extensions

Data corrected by Giovanni Resta, Apr 21 2017

Status

approved