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 1-5 of 5 results.

A080504 Triangle whose n-th row contains the least set (ordered lexicographically) of n distinct positive integers whose arithmetic and geometric means are both integers.

Original entry on oeis.org

1, 1, 9, 1, 2, 108, 1, 2, 5, 1000, 1, 2, 3, 4, 1012500, 1, 2, 3, 4, 8, 15552, 1, 2, 3, 4, 5, 6, 25015118625000, 1, 2, 3, 4, 5, 6, 11, 17757684573750000, 1, 2, 3, 4, 5, 6, 7, 8, 19699405917187500, 1, 2, 3, 4, 5, 6, 7, 8, 14, 295491088757812500, 1, 2, 3, 4, 5, 6, 7
Offset: 1

Views

Author

Amarnath Murthy, Mar 20 2003

Keywords

Comments

Row n has the form {1,2,...,n-2,x,y} where n-1 <= x < y. x is minimal such that y exists.

Examples

			The fourth row contains 1,2,5,1000, with AM=252 and GM=10. There is no set of the form {1,2,3,y} or {1,2,4,y} whose AM and GM are both integers.

Crossrefs

Cf. A080505, A081556, A080506, A080507, A080508, A080511.

A080505 Last term in n-th row of A080504.

Original entry on oeis.org

1, 9, 108, 1000, 1012500, 15552, 25015118625000, 17757684573750000, 19699405917187500, 295491088757812500, 2754030502015722328328015625000, 69471494082638078965978431093750000
Offset: 1

Views

Author

Amarnath Murthy, Mar 20 2003

Keywords

Crossrefs

Cf. A080504, A081556, A080506, A080507.

A080506 Geometric mean of n-th row of A080504.

Original entry on oeis.org

1, 3, 6, 10, 30, 12, 210, 330, 210, 210, 2310, 3570, 30030, 2310, 30030, 690690, 510510, 30030, 9699690, 14804790, 9699690, 19399380, 223092870, 9699690, 223092870, 223092870, 223092870, 9146807670, 6469693230, 223092870
Offset: 1

Views

Author

Amarnath Murthy, Mar 20 2003

Keywords

Crossrefs

Cf. A080504, A080505, A081556, A080507.

A080507 Arithmetic mean of n-th row of A080504.

Original entry on oeis.org

1, 5, 37, 252, 202502, 2595, 3573588375003, 2219710571718754, 2188822879687504, 29549108875781255, 250366409274156575302546875005, 5789291173553173247164869257812506
Offset: 1

Views

Author

Amarnath Murthy, Mar 20 2003

Keywords

Crossrefs

Cf. A080504, A080505, A081556, A080506.

A187012 Antidiagonal sums of A103516.

Original entry on oeis.org

1, 2, 5, 4, 8, 6, 11, 8, 14, 10, 17, 12, 20, 14, 23, 16, 26, 18, 29, 20, 32, 22, 35, 24, 38, 26, 41, 28, 44, 30, 47, 32, 50, 34, 53, 36, 56, 38, 59, 40, 62, 42, 65, 44, 68, 46, 71, 48, 74, 50, 77, 52, 80, 54, 83, 56, 86, 58, 89, 60, 92, 62, 95, 64
Offset: 2

Views

Author

Michel Marcus, Aug 30 2013

Keywords

Comments

This sequence differs from A081556 at least for n=24 (see comment about n=24 in A081556).

Links

Programs

  • Mathematica
    CoefficientList[Series[(1 + 2 x + 3 x^2 - x^4)/((1 - x)^2 (1 + x)^2), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 24 2014 *)
  • PARI
    a(n) = sum(k=0, n\2, 0^(k*(n-2*k))*(n-k+1)); \\ Michel Marcus, Aug 30 2013

Formula

a(n) = sum{k=0..floor(n/2), 0^(k(n-2k))*(n-k+1)}. - Paul Barry, Aug 30 2013
G.f. : x^2*(1+2*x+3*x^2-x^4)/((1-x)^2*(1+x)^2).
a(n) = A080512(n) - 1 for n>2.
Showing 1-5 of 5 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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