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.

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A230400 Numbers n such that n = abc = 2(ab+ac+bc) for some positive integers a,b,c.

Original entry on oeis.org

216, 250, 256, 288, 400, 432, 450, 486, 576, 882
Offset: 1

Views

Author

M. F. Hasler, Oct 18 2013

Keywords

Comments

Otherwise said: Volumes of integer-sided cubes equal to their surface area (assuming dimensionless unit of length).
The sequence is a finite subsequence of A055744, A069167, A073539, A090779 and A137845.

Examples

			The triples (a,b,c) ordered by largest member(s) are (6,6,6), (8,8,4), (10,5,5), (12,6,4), (12,12,3), (15,10,3), (18,9,3), (20,5,4), (24,8,3), (42,7,3).

Links

Crossrefs

Cf. A229941.

Programs

  • PARI
    L=[];for(a=1,99,for(b=1,a,for(c=1,b,a*b*c==2*(a*b+b*c+a*c)&&!printf("(%d,%d,%d), ",a,b,c)&&L=concat(L,a*b*c))));vecsort(L)

A260819 Positive integer solutions [a',b',c',d'] of the equation 1/a + 1/b + 1/c + 1/d = 1, for a <= b <= c <= d, lexicographically sorted.

Original entry on oeis.org

2, 3, 7, 42, 2, 3, 8, 24, 2, 3, 9, 18, 2, 3, 10, 15, 2, 3, 12, 12, 2, 4, 5, 20, 2, 4, 6, 12, 2, 4, 8, 8, 2, 5, 5, 10, 2, 6, 6, 6, 3, 3, 4, 12, 3, 3, 6, 6, 3, 4, 4, 6, 4, 4, 4, 4
Offset: 1

Views

Author

Marco Ripà, Jul 31 2015

Keywords

Comments

There are only 14 positive integer solutions for 1/a + 1/b + 1/c + 1/d = 1.

Examples

			The 2nd row is [2,3,8,24] and represents the solution 1/2 + 1/3 + 1/8 + 1/24 = 1.
List of all the solutions:
1/2 + 1/3 + 1/7  + 1/42 = 1
1/2 + 1/3 + 1/8  + 1/24 = 1
1/2 + 1/3 + 1/9  + 1/18 = 1
1/2 + 1/3 + 1/10 + 1/15 = 1
1/2 + 1/3 + 1/12 + 1/12 = 1
1/2 + 1/4 + 1/5  + 1/20 = 1
1/2 + 1/4 + 1/6  + 1/12 = 1
1/2 + 1/4 + 1/8  + 1/8  = 1
1/2 + 1/5 + 1/5  + 1/10 = 1
1/2 + 1/6 + 1/6  + 1/6  = 1
1/3 + 1/3 + 1/4  + 1/12 = 1
1/3 + 1/3 + 1/6  + 1/6  = 1
1/3 + 1/4 + 1/4  + 1/6  = 1
1/4 + 1/4 + 1/4  + 1/4  = 1

References

  • W. Sierpiński, 250 problems in elementary number theory, Elsevier Science Ltd, pages 14 and 83-85.

Links

Crossrefs

Cf. A229941.
Showing 1-2 of 2 results.

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