A191383
Integers n such that each of n, 2n and 3n is a sum of 2 distinct positive cubes.
Original entry on oeis.org
2457, 15561, 19656, 25389, 39816, 66339, 124488, 157248, 203112, 248976, 307125, 318528, 420147, 530712, 685503, 842751, 995904, 1075032, 1257984, 1624896, 1791153, 1945125, 1991808, 2457000, 2548224, 3173625, 3270267
Offset: 1
2457 is in the sequence because 2457 = 9^3+12^3, 2*2457 = 4914 = 1^3+17^3, 3*2457 = 7371 = 8^3+19^3 have at least one representation as a sum of two distinct positive cubes.
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isA000578 := proc(n) option remember; local f; for f in ifactors(n)[2] do if op(2,f) mod 3 <> 0 then return false; end if; end do: true ; end proc:
isA024670 := proc(n) option remember ; local k,kc,k3 ; for k from 1 do k3 := k^3 ; kc := n-k^3 ; if kc <= k3 then return false; elif isA000578(kc) then return true; end if; end do: end proc:
isA191383 := proc(n) isA024670(n) and isA024670(2*n) and isA024670(3*n) ; end proc:
for n from 1 do if isA191383(n) then printf("%d,\n",n); end if; end do: # R. J. Mathar, Jun 03 2011
A273753
Taxi-cab numbers (A001235) that are the average of two positive cubes in more than one way.
Original entry on oeis.org
6742008, 53936064, 182034216, 431488512, 842751000, 1456273728, 1581292125, 2312508744, 3451908096, 4914923832, 6742008000, 8973612648, 11395366632, 11650189824, 12650337000, 14812191576, 18500069952, 22754277000, 27615264768, 33123485304, 39319390656
Offset: 1
6742008 is a term because 6742008 = 46^3 + 188^3 = 126^3 + 168^3 = (14^3 + 238^3)/2 = (105^3 + 231^3)/2.
53936064 is a term because 53936064 = 2^3*6742008.
1581292125 is a term because 1581292125 = 50^3 + 1165^3 = 540^3 + 1125^3 = (435^3 + 1455^3)/2 = (909^3 + 1341^3)/2.
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T = thueinit(x^3+1, 1);
isA001235(n) = my(v=thue(T, n)); sum(i=1, #v, v[i][1]>=0 && v[i][2]>=v[i][1])>1;
isok(n) = isA001235(n) && isA001235(2*n);
A282948
Numbers n such that (u^4 + v^4)/2 = x^4 + y^4 = n has a solution in positive integers u,v,x,y.
Original entry on oeis.org
162401, 2598416, 13154481, 41574656, 101500625, 210471696, 389924801, 665194496, 1065512961, 1624010000, 2377713041, 3367547136, 4638334961, 6238796816, 8221550625, 10643111936, 13563893921, 17048207376, 21164260721, 25984160000, 31583908881, 38043408656
Offset: 1
(19^4 + 21^4)/2 = 7^4 + 20^4 = 162401.
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isA003336(n) = for(k=1, sqrtnint(n\2, 4), ispower(n-k^4, 4) && return(1));
is(n) = isA003336(n) && isA003336(2*n);
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T=thueinit('x^4+1, 1);
has(n)=#thue(T, n)>0 && !issquare(n)
list(lim)=my(v=List(),x4,t); for(x=1,sqrtnint(lim\=1,4), x4=x^4; for(y=1,min(sqrtnint(lim-x4,4),x), t=x4+y^4; if(has(2*t), listput(v,t)))); Set(v) \\ Charles R Greathouse IV, Feb 26 2017
A189821
Smallest integer m such that m*j is a sum of two distinct positive cubes for j=1..n.
Original entry on oeis.org
9, 728, 2457, 124488, 124488, 124488
Offset: 1
a(6)=m=124488: 1*m=124488=34^3+44^3, 2*m=248976=22^3+62^3, 3*m=373464=6^3+72^3=54^3+60^3, 4*m=497952=17^3+79^3, 5*m=622440=37^5+83^3, 6*m=746928=71^3+73^3.
Showing 1-4 of 4 results.
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