cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

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

Views

Author

Zak Seidov, Jun 01 2011

Keywords

Examples

			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.
		

Crossrefs

Programs

  • Maple
    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

Formula

{n: n in A024670 and 2n in A024670 and 3n in A024670}.

A191367 a(n) is the smallest sum of 2 distinct positive cubes such that n*a(n) is also sum of 2 distinct positive cubes.

Original entry on oeis.org

9, 728, 2457, 189, 189, 126, 91, 9, 1001, 28, 91, 126, 133, 9, 2331, 91, 91, 189, 91, 854, 9, 133, 133, 2457, 217, 28, 9, 126, 217, 468, 133, 189, 3528, 11772, 637, 28, 133, 28, 9, 189, 637, 468, 217, 559, 152, 637, 559, 126, 72, 637, 5256, 9, 793, 28, 793
Offset: 1

Views

Author

Zak Seidov, Jun 01 2011

Keywords

Comments

a(n) and n*a(n) are terms of A024670 (Numbers that are sums of 2 distinct positive cubes); a(n)=9 if n is in A191352.

Examples

			{n,a(n),b,c,n*a(n),d,e}={1,9,1,2,9,1,2},{2,728,6,8,1456,5,11},{3,2457,9,12,7371,8,19},...
		

Crossrefs

Formula

a(n)=b^3+c^3, n*a(n)=d^3+e^3.

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

Views

Author

Zak Seidov, Jun 02 2011

Keywords

Comments

Identifies the first arithmetic progression with at least n terms in A024670.
Terms beyond a(6) are >= 1400000 (but may not exist).

Examples

			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.
		

Crossrefs

Showing 1-3 of 3 results.