A206606 -id:A206606 - cp's OEIS frontend

A162930 Primes that can be written as a sum of a positive square and a positive cube in more than one way.

17, 89, 233, 449, 577, 593, 1289, 1367, 1601, 1753, 2089, 2521, 3391, 4481, 4721, 5953, 6121, 6427, 7057, 7577, 8081, 9649, 10313, 10657, 10729, 11969, 12329, 13121, 13457, 15137, 15193, 15641, 15661, 16033, 16649, 18523, 21673, 21961, 23201

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jul 17 2009

nonn

A subset of these, 2089, 4481, 7057, 15193, 15641, etc., allows this representation in more than two ways (See A206606).

			The prime 17 can be written 1^3 + 4^2 as well as 2^3 + 3^2.

David A. Corneth, Table of n, a(n) for n = 1..10808 (first 500 terms from Seiichi Manyama, terms <= 8*10^7)

Cf. A000040, A054402, A123364, A123388, A173795, A206606.

isA162930 := proc(n) if isprime(n) then wa := 0 ; for y from 1 to n/2 do if issqr(n-y^3) then if n -y^3 > 0 then wa := wa+1 ; fi; fi; od: RETURN( wa>1) ; else false; fi; end:
for i from 1 to 2700 do if isA162930 ( ithprime(i)) then printf("%d,",ithprime(i)) ; fi; od: # R. J. Mathar, Jul 21 2009

lst={};Do[Do[AppendTo[lst,n^2+m^3],{n,2*5!}],{m,2*5!}];lst=Sort[lst]; lst2={};Do[If[lst[[n]]==lst[[n+1]]&&PrimeQ[lst[[n]]],AppendTo[lst2, lst[[n]]]],{n,Length[lst]-1}];lst2;

upto(n) = {my(res = List(), v = vector(n), i, j, i2); for(i = 1, sqrtint(n), i2 = i^2; for(j = 1, sqrtnint(n - i^2, 3), v[i2 + j^3]++)); forprime(p = 2, n, if(v[p] > 1, listput(res, p))); kill(v); res} \\ David A. Corneth, Jun 20 2023

A000040 INTERSECT A054402.

Slightly edited by R. J. Mathar, Jul 21 2009

A207650 Squares that can be written as a sum of 3 distinct nonzero squares in 3 or more ways.

Original entry on oeis.org

441, 529, 729, 841, 961, 1089, 1225, 1369, 1521, 1681, 1764, 1849, 2025, 2116, 2209, 2401, 2601, 2809, 2916, 3025, 3249, 3364, 3481, 3721, 3844, 3969, 4225, 4356, 4489, 4761, 4900, 5041, 5329, 5476, 5625, 5929, 6084, 6241, 6561, 6724, 6889, 7056, 7225, 7396

Offset: 1

Vladimir Joseph Stephan Orlovsky, Feb 19 2012

nonn

Cf. A161992, A206606, A207638, A207639, A207640.

t = Sort@Select[Flatten[Table[x^2 + y^2 + z^2, {x, 400}, {y, x + 1, 400}, {z, y + 1, 400}]], # < 160006 && IntegerQ[Sqrt[#]] &];
f1[l_] := Module[{t = {}}, Do[If[l[[n]] != l[[n + 1]] && l[[n]] != l[[n - 1]], AppendTo[t, l[[n]]]], {n, Length[l] - 1}]; t];
f2[l_] := Module[{t = {}}, Do[If[l[[n]] == l[[n + 1]], AppendTo[t, l[[n]]]], {n, Length[l] - 1}]; t];
s1 = Join[{First[t]}, f1[t]];
Complement[t, s1];
t = f2[t];
s2 = Join[{First[t]}, f1[t]];
Complement[t, s2]

cp's OEIS Frontend

A162930 Primes that can be written as a sum of a positive square and a positive cube in more than one way.

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