A206476 Numbers n such that n^5 = a^2 + b^3 + c^5 for some positive integers a, b, and c.

2, 6, 8, 9, 10, 11, 12, 13, 14, 18, 19, 20, 21, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 59, 60, 61, 62, 64, 65, 66, 67, 68, 69

Offset

1,1

Comments

Some can be expressed in more than one way.

Links

Table of n, a(n) for n=1..55.

Example

10^5 = 168^2 + 40^3 + 6^5 = 280^2 + 24^3 + 6^5.

Prog

(Maxima) isA206476(n) := block(
    [a, b, c, v],
    v : false ,
    for c : 1 while c < n and not v do (
        for b : 1 while b^3+c^5 < n^5 and not v do (
            for a : isqrt(n^5-c^5-b^3) while a^2+b^3+c^5 <= n^5 and not v do (
                if equal(a^2+b^3+c^5, n^5) then v : true
            )
        )
    ),
    return(v)
)$
for n : 1 thru 100 do (
    if equal(isA206476(n), true ) then print(n)
)$ /* R. J. Mathar, Feb 27 2012 */

Crossrefs

Sequence in context: A320573 A003610 A201776 * A077477 A095879 A342751

Adjacent sequences: A206473 A206474 A206475 * A206477 A206478 A206479

Keyword

nonn

Author

Carmine Suriano, Feb 08 2012

Status

approved