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.

A114694 Numbers n such that A055081(n) = A055081(n+1).

Original entry on oeis.org

3, 4, 51, 68, 92, 99, 115, 123, 175, 212, 235, 236, 267, 291, 355, 403, 411, 412, 427, 451, 452, 596, 628, 656, 668, 716, 723, 763, 771, 788, 843, 860, 884, 892, 916, 932, 955, 964, 1003, 1027, 1076, 1132, 1220, 1227, 1235, 1243, 1252, 1267, 1347, 1348
Offset: 1

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Author

Zak Seidov, Dec 25 2005

Keywords

Comments

There are numbers n such that A055081(n) = A055081(n+1) = A055081(n+2), e.g., A055081(91323)=A055081(91324)=A055081(91325)=47; but apparently there are no n's such that A055081(n) = A055081(n+1) = A055081(n+2) = A055081(n+3). Cf. A055081 Number of positive integers whose harmonic mean with n is a positive integer, A114585 Minimal numbers m such that number of positive integers whose harmonic mean with m is n.

Crossrefs

Cf. A055081, A114585.

A066761 Number of positive integers of the form (n^2+k^2)/(n-k) for k=1,2,3,4,....,n-1.

Original entry on oeis.org

1, 2, 2, 2, 4, 2, 3, 4, 5, 2, 7, 2, 5, 7, 4, 2, 8, 2, 7, 8, 5, 2, 10, 4, 5, 6, 7, 2, 15, 2, 5, 8, 5, 7, 13, 2, 5, 8, 10, 2, 15, 2, 8, 12, 5, 2, 13, 4, 9, 8, 8, 2, 12, 8, 10, 8, 5, 2, 23, 2, 5, 13, 6, 8, 15, 2, 8, 8, 16, 2, 17, 2, 5, 13, 8, 7, 16, 2, 13, 8, 5, 2, 23, 8, 5, 8, 10, 2, 26, 7, 8, 8, 5, 8
Offset: 2

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Author

Benoit Cloitre, Jan 17 2002

Keywords

Comments

Also the number of factors of 2*n^2 which are less than n. - Vladeta Jovovic, Dec 12 2002
Also the number of factors of 2*n^2 which are greater than 2*n, so a(n) = tau(2*n^2)-1-A055081(n). - Vladeta Jovovic, Dec 13 2002

Examples

			a(2)=1 because (2^2+1)/(2-1) is the only integer of this form.

Formula

No general formula is known but let k be a positive integer, p and q distinct odd primes then a(2^k)=k a(p^k)=2*k a(p*q)= 7 or 8 if p >13 a(2*p)= 5 if p>5 a(9*p^2)= 23 .... Asymptotic formula: (1/n)*sum(i=1, n, a(i))= log(n)*log(log(n))+o(log(n)).

Extensions

Corrected by Vladeta Jovovic, Dec 12 2002

A114585 Minimal numbers m such that number of positive integers whose harmonic mean with m is n.

Original entry on oeis.org

1, 2, 3, 8, 9, 10, 6, 128, 21, 12, 18, 136, 24, 250, 54, 36, 45, 230, 70, 30, 200, 72, 135, 32896, 384, 441, 144, 324, 105, 60, 490, 150, 90, 972, 1215, 3087, 576, 408, 168, 120, 3645, 1152, 3430, 750, 270, 378, 735, 300, 180, 35937, 9261, 1728, 882, 450, 8990
Offset: 1

Views

Author

Zak Seidov, Dec 10 2005

Keywords

Comments

Also minimal numbers m such that the number of factors of 2 m^2 which are less than 2 m, is n. First missed entry is for n=60, m>100000. Cf. A055081 Number of positive integers whose harmonic mean with n is a positive integer.

Crossrefs

Greedy inverse of A055081.
Showing 1-3 of 3 results.

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

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