Revision History for A274062
(Underlined text is an addition;
strikethrough text is a deletion.)
Showing entries 1-10
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#16 by N. J. A. Sloane at Fri Jun 17 00:44:36 EDT 2016
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#15 by Michel Marcus at Tue Jun 14 06:10:36 EDT 2016
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Discussion
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| Tue Jun 14
| 11:24
| Michel Lagneau: Thanks Michel !
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#14 by Michel Marcus at Tue Jun 14 06:10:20 EDT 2016
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| KEYWORD
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nonn,more,changed
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Discussion
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| Tue Jun 14
| 06:10
| Michel Marcus: I've got more terms behind
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#13 by Michel Marcus at Tue Jun 14 06:09:58 EDT 2016
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| DATA
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2, 14, 18, 230, 238, 4958, 53430, 57930, 64506, 65586, 68226, 70730, 77270, 78638, 81926, 84986, 88826, 90446, 91306, 1006350, 1248054, 1341950, 18177726, 19033854, 19603430, 21044030, 22356798, 22395522, 22876730, 23954170, 24241966, 24840710, 24883910, 25285666, 25306246
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| EXTENSIONS
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a(23)-a(35) from Michel Marcus, Jun 14 2016
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proposed
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#12 by Michel Marcus at Thu Jun 09 10:52:32 EDT 2016
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Discussion
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| Thu Jun 09
| 10:54
| Michel Marcus: Up to where did you search ?
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| 11:33
| Michel Lagneau: No other terms < 2*10^6.
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| 12:08
| Michel Marcus: No other terms < 10^7
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| 12:28
| Michel Lagneau: OK Michel.
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#11 by Michel Marcus at Thu Jun 09 10:49:03 EDT 2016
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| PROG
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(PARI) isok(n) = sod = sumdiv(n, d, d*(d % 2)); (2*sod == sumdiv(n, d, d*(1-(d % 2)))) && (issquare(5*sod^2-4) || issquare(5*sod^2+4)); \\ Michel Marcus, Jun 09 2016
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#10 by Michel Marcus at Thu Jun 09 10:37:13 EDT 2016
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#9 by Michel Marcus at Thu Jun 09 10:33:15 EDT 2016
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| COMMENTS
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The sequence is generalizable with the following definition: even numbers such that the sum of the odd divisors is a Fibonacci number F and the sum of the even divisors is (2^k -2)*F = A000918(k)*F with k>1. The corresponding sequences b(n,k) are of the form b(n,k) = a(n)*2^(k-2) where a(n) is the primitive sequence.
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| EXAMPLE
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18 is in the sequence because the: its divisors are {1, 2, 3, 6, 9, 18}, }; the sum of theits odd divisors is 1 + 3 + 9 = 13 is , a Fibonacci number , and the sum of theits even divisors is 2 + 6 + 18 = 26 = 2*13.
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#8 by Michael De Vlieger at Thu Jun 09 09:58:13 EDT 2016
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#7 by Michael De Vlieger at Thu Jun 09 09:58:09 EDT 2016
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| MATHEMATICA
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t = Fibonacci@ Range@ 40; Select[Range[2, 2*10^6, 4], Function[d, And[Total@ Select[d, EvenQ] == 2 #, MemberQ[t, #]] &@ Total@ Select[d, OddQ]]@ Divisors@ # &] (* Michael De Vlieger, Jun 09 2016 *)
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