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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
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
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
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