

A058957


Numbers having at least two representations as b^2  c^2 with b > c >= 0.


6



9, 15, 16, 21, 24, 25, 27, 32, 33, 35, 36, 39, 40, 45, 48, 49, 51, 55, 56, 57, 60, 63, 64, 65, 69, 72, 75, 77, 80, 81, 84, 85, 87, 88, 91, 93, 95, 96, 99, 100, 104, 105, 108, 111, 112, 115, 117, 119, 120, 121, 123, 125, 128, 129, 132, 133, 135, 136, 140, 141, 143
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OFFSET

1,1


COMMENTS

This is the union of the squares > 4 and A306102: numbers that are the difference of two positive squares in at least two ways (where c=0 is excluded).  M. F. Hasler, Jul 12 2018


LINKS

Table of n, a(n) for n=1..61.


FORMULA

A058957 = { n  A034178(n) >= 2 }.  M. F. Hasler, Jul 10 2018


EXAMPLE

9 is in the sequence since 9 = 3^2  0^2 = 5^2  4^2;
45 is in the sequence since 45 = 7^2  2^2 = 9^3  6^2 = 23^2  22^2.


MATHEMATICA

Select[Range@143, Length@ FindInstance[x^2  y^2 == # && x>y>= 0, {x, y}, Integers, 2] == 2 &] (* Giovanni Resta, Jul 10 2018 *)


PROG

(PARI) select( is(n)=fordiv(n, d, d^2 > n && return; (nd^2)%(2*d)  c++<2  return(1)), [1..200]) \\ M. F. Hasler, Jul 10 2018


CROSSREFS

Cf. A034178, A016825.
Cf. A306102 (subsequence and variant using c > 0).
Sequence in context: A232395 A184048 A284128 * A257409 A105882 A136410
Adjacent sequences: A058954 A058955 A058956 * A058958 A058959 A058960


KEYWORD

nonn


AUTHOR

Henry Bottomley, Jan 13 2001


EXTENSIONS

Name edited by M. F. Hasler, Jul 10 2018


STATUS

approved



