A180480 Numbers n such that n*n/k is an integer. n=(x_1 x_2 ... x_r) where x_i are digits of n, k = x_1^2 + x_2^2 + ... + x_r^2.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 111, 114, 120, 130, 133, 170, 200, 210, 220, 222, 228, 240, 260, 266, 267, 298, 300, 310, 315, 330, 333, 340, 360, 372, 376, 390, 399, 400, 420, 430, 440, 444, 480, 500, 532, 550, 555, 600

Offset

1,2

Links

Ivan Neretin, Table of n, a(n) for n = 1..10000

Example

n=267, 267*267/(2*2+6*6+7*7)=801, n=267 belongs to the sequence.

Maple

filter:= proc(n)
  type(n^2/convert(map(`^`, convert(n, base, 10), 2), `+`), integer)
end proc:
select(filter, [$1..1000]); # Robert Israel, Aug 03 2015

Mathematica

Select[Range[600], Divisible[#^2, Plus @@ (IntegerDigits[#]^2)] &] (* Ivan Neretin, Aug 03 2015 *)

Prog

(PARI) k(n)=apply(sqr, digits(n));
is_ok(n)=my(kk=vecsum(k(n))); n*n\kk===n*n/kk;
first(m)=my(v=vector(m), k=1); for(i=1, m, while(!is_ok(k), k++); v[i]=k; k++); v; \\ Anders Hellström, Aug 03 2015

Crossrefs

Cf. A005349

Sequence in context: A352461 A302768 A202272 * A080459 A093475 A032571

Adjacent sequences: A180477 A180478 A180479 * A180481 A180482 A180483

Keyword

base,easy,nonn

Author

Ctibor O. Zizka, Sep 07 2010

Status

approved