The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A068346 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A068346

a(n) = n'' = second arithmetic derivative of n.
(history; published version)

#43 by Michel Marcus at Mon Oct 16 14:35:43 EDT 2023

STATUS

editing

proposed

Discussion

Mon Oct 16

14:43

Amiram Eldar: I am not getting that 1133568 is a record: a(1133568) = 41859072 < 45088768 = a(524288).

14:46

Amiram Eldar: No. I made a mistake. 1133568 is indeed a record value and not in A116882. The record values are 4, 16, 32, 80, 176, 240, 640, 1408, 1472, 2368, 5120, 10752, 13568, 26624, 29952, 34560, 57344, 114688, 167936, 191488, 245760, 323584, 380928, 471040, 819200, 1011712, 1133568, ...

14:48

Amiram Eldar: Maybe you mean "positions of records" and not "record values"?

#42 by Michel Marcus at Mon Oct 16 14:35:39 EDT 2023

STATUS

proposed

editing

#41 by Michel Marcus at Tue Oct 03 10:27:40 EDT 2023

STATUS

editing

proposed

Discussion

Mon Oct 16

14:29

Michel Marcus: limited data points (22) ? : no, there is a b-file in both sequences; and you have code in A003415 ; and a(n) = A003415 (A003415 (n))

14:33

Michel Marcus: I wrote these: isok(n) = 2^(valuation(n, 2)*2) >= n; \\ A116882
ader(n) = local(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1])); \\ A003415(
a(n) = ader(ader(n));
lista(nn) = my(r=0); for (n=1, nn, my(m=ader(ader(n))); if (m>r, r=m; if (!isok(r), print1(r, ", "))););

14:34

Michel Marcus: and I got 1133568 a record that is not in A116882; can you check ?  or someone else ?

#40 by Michel Marcus at Tue Oct 03 10:27:18 EDT 2023

COMMENTS

a(A000040(n)) = 0; a(A157037(n)) = 1. - Reinhard Zumkeller, Feb 22 2009

a(n) records Records > 0 appear to all belong to A116882. - Bill McEachen, Oct 03 2023

FORMULA

a(A000040(n)) = 0; a(A157037(n)) = 1. - Reinhard Zumkeller, Feb 22 2009

STATUS

proposed

editing

#39 by Bill McEachen at Tue Oct 03 10:21:00 EDT 2023

STATUS

editing

proposed

#38 by Bill McEachen at Tue Oct 03 10:20:30 EDT 2023

COMMENTS

a(n) records > 0 appear to all belong to A116882. - Bill McEachen, Oct 03 2023

STATUS

approved

editing

Discussion

Tue Oct 03

10:20

Bill McEachen: I have no insight into either seq otherwise, limited data points (22) and no Pari script

#37 by Alois P. Heinz at Tue Aug 29 14:43:29 EDT 2017

STATUS

proposed

approved

#36 by Michel Marcus at Tue Aug 29 12:49:34 EDT 2017

STATUS

editing

proposed

#35 by Michel Marcus at Tue Aug 29 12:49:11 EDT 2017

LINKS

Victor Ufnarovski and Bo Ahlander, Åhlander, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL6/Ufnarovski/ufnarovski.html">How to Differentiate a Number</a>, J. Integer Seqs., Vol. 6, 2003.

STATUS

proposed

editing

#34 by Alois P. Heinz at Tue Aug 29 12:38:36 EDT 2017

STATUS

editing

proposed