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A162869 Primes of the form (x^2 + y^3)/(x+y), with x,y > 1 two distinct integers. 0
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 (list; graph; refs; listen; history; text; internal format)
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: A243765 A256148 A083520 * A079018 A002383 A163418

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

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Last modified September 20 17:04 EDT 2020. Contains 337265 sequences. (Running on oeis4.)