The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A251758 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A251758

Let n>=2 be a positive integer with divisors 1 = d_1 < d_2 < ... < d_k = n, and s = d_1*d_2 + d_2*d_3 + ... + d_(k-1)*d_k. The sequence lists the values a(n) = floor(n^2/s).
(history; published version)

#77 by Jon E. Schoenfield at Sat Sep 09 19:27:44 EDT 2017

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editing

approved

#76 by Jon E. Schoenfield at Sat Sep 09 19:27:41 EDT 2017

FORMULA

a(n) <= A250480(n), and especially, for all composite n, a(n) < A020639(n). [Cf. the comments-Comments section above.] - Antti Karttunen, Dec 09 2014

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editing

#75 by Jon E. Schoenfield at Sat Mar 28 16:01:42 EDT 2015

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approved

#74 by Jon E. Schoenfield at Sat Mar 28 16:01:37 EDT 2015

COMMENTS

Conjecture: Terms x, where a(x)=n, x=p#k/p#j, p#i is the i_-th primorial, k>j is suitable large k and j is the number of primes less than n. As an example, n=9, x = p#7/p#4 = 2431. For n=10, x = p#6/p#4 = 143 although 121 = 11^2 is the least x where a(x)=10 (see formula section). For n=8, x = p#12/p#4, p#13/p#4, p#14/p#4, p#15/p#4, p#16/p#4, etc. But is p#12/p#4 the least such x? - Robert G. Wilson v, Dec 18 2014

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approved

editing

#73 by N. J. A. Sloane at Thu Jan 15 13:11:11 EST 2015

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approved

#72 by Jon E. Schoenfield at Sat Dec 20 15:48:45 EST 2014

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#71 by Jon E. Schoenfield at Sat Dec 20 15:48:41 EST 2014

EXTENSIONS

Comments section edited by Antti Karttunen, Dec 09 2014.

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#70 by Antti Karttunen at Fri Dec 19 07:20:07 EST 2014

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#69 by Antti Karttunen at Fri Dec 19 07:17:55 EST 2014

EXTENSIONS

Comments section edited by Antti Karttunen, Dec 09 2014.

Instances of n for which a(n) = 8 and 14 found by Robert G. Wilson v, Dec 18 2014

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proposed

editing

Discussion

Fri Dec 19

07:20

Antti Karttunen: @Robert: Added to the Extensions-section a note that it was you found the instances of n for which a(n) = 8 and a(n) = 14.

#68 by Jon E. Schoenfield at Thu Dec 18 20:11:10 EST 2014

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editing

proposed