A067521 Numbers n such that the square root of n is an integer and a multiple of the sum of the digits of n.

1, 81, 100, 324, 400, 1296, 2025, 2401, 2704, 2916, 4225, 5184, 6400, 7744, 8100, 10000, 11664, 12544, 20736, 26244, 32400, 33124, 36100, 39204, 40000, 46656, 59049, 63504, 72900, 75625, 88209, 104329, 104976, 122500, 123201, 129600

Offset

1,2

Links

Mehrad Mahmoudian, Table of n, a(n) for n = 1..10000

Mehrad Mahmoudian, R code to produce the sequence

Example

18^2=324, 18=2*(3+2+4), so 324 is in the sequence.

Maple

dig := X->convert((convert(X, base, 10)), `+`); seq(`if`(isprime(i)=false, `if`(i mod dig(i^2)=0, i^2, NULL), NULL), i=1..1000);

Mathematica

Select[Range[500]^2, Divisible[Sqrt[#], Total[IntegerDigits[#]]]&] (* Harvey P. Dale, Jul 15 2013 *)

Crossrefs

Subsequence of squares (A000290).

Cf. A067520 (similar for triangular numbers).

Sequence in context: A335066 A179444 A068834 * A117686 A104113 A102766

Adjacent sequences: A067518 A067519 A067520 * A067522 A067523 A067524

Keyword

base,easy,nonn

Author

Amarnath Murthy, Feb 14 2002

Extensions

More terms from Sascha Kurz and Francois Jooste (phukraut(AT)hotmail.com), Mar 18 2002

Definition corrected by Harvey P. Dale, Jul 15 2013

Status

approved