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A134657 Numbers of the form p^2 + q^3 + r^4 with p, q and r primes.

%I A134657 #13 Feb 21 2020 20:10:49
%S A134657 28,33,47,49,52,68,73,92,93,98,112,114,117,133,138,145,150,157,164,
%T A134657 166,190,193,210,212,215,229,231,255,258,262,277,310,313,327,332,363,
%U A134657 368,375,378,384,385,397,404,408,428,430,433,449,450,469,473,480,495
%N A134657 Numbers of the form p^2 + q^3 + r^4 with p, q and r primes.
%C A134657 The primes p, q, and r are not necessarily distinct. - _Jon E. Schoenfield_, Sep 24 2018
%H A134657 Project Euler, <a href="https://projecteuler.net/index.php?section=problems&amp;id=87">Problem 87: Prime power triples</a>.
%e A134657 a(1) = 28 = 2^2 + 2^3 + 2^4 is the smallest sum of a prime squared, a prime cubed and the 4th power of a prime.
%e A134657 a(2) = 33 = 3^2 + 2^3 + 2^4 is the next number of that form.
%t A134657 Take[Union[Total[#^{2,3,4}]&/@Tuples[Prime[Range[10]],3]],60] (* _Harvey P. Dale_, Mar 02 2013 *)
%o A134657 (PARI) is_p87(n,t,tt)=forprime(p=2,sqrtn(n,4),t=n-p^4; forprime(q=2,sqrtn(t,3), issquare(t-q^3,&tt) || next; isprime(tt) && return(1)))
%o A134657 print_p87(Nmax=999)=for(n=1,Nmax,is_p87(n) && print1(n","))
%Y A134657 Cf. A045701.
%K A134657 easy,nonn
%O A134657 1,1
%A A134657 _M. F. Hasler_, Jan 25 2008