A162869 Primes of the form (x^2 + y^3)/(x+y), with x,y > 1 two distinct integers.

3, 7, 13, 31, 43, 67, 73, 109, 139, 149, 157, 179, 193, 211, 229, 241, 307, 317, 379, 389, 421, 457, 463, 491, 499, 593, 601, 647, 661, 751, 757, 769, 829, 839, 937, 1009, 1021, 1033, 1123, 1171, 1213, 1231, 1283, 1319, 1381, 1459, 1481, 1483, 1549, 1621

Offset

1,1

Links

Table of n, a(n) for n=1..50.

Example

a(1) = 3 = (1^2 + 2^3)/(1+2).
a(2) = 7 = (1^2 + 3^3)/(1+3) or (6^2 + 3^3)/(6+3).
a(3) = 13 = (1^2 + 4^3)/(1+4) or (12^2 + 4^3)/ (12+4).
a(4) = 31 = (1^2 + 6^3)/(1+6).

Maple

isA162869 := proc(p) local a, b ; if isprime(p) then for b from 1 to p do for d in numtheory[divisors](b^2*(b+1)) do a := d-b ; if a > 1 and (a^2+b^3)= p*(a+b) then RETURN(true); fi; od: od: RETURN(false) ; else false; fi; end:
for n from 1 do p := ithprime(n) ; if isA162869(p) then printf("%d, \n", p) ; fi; od: # R. J. Mathar, Sep 22 2009

Mathematica

f[a_, b_]:=(a^2+b^3)/(a+b); lst={}; Do[Do[If[f[a, b]==IntegerPart[f[a, b]], If[a!=b&&PrimeQ[f[a, b]], AppendTo[lst, f[a, b]]]], {b, 4*6!}], {a, 4*6!}]; Take[Union[lst], 50]

Crossrefs

Sequence in context: A256148 A083520 A336801 * A079018 A342150 A002383

Adjacent sequences: A162866 A162867 A162868 * A162870 A162871 A162872

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Jul 15 2009

Extensions

Comment turned into examples by R. J. Mathar, Sep 22 2009

Status

approved