Revision History for A127666
(Underlined text is an addition;
strikethrough text is a deletion.)
Showing entries 1-10
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#23 by Peter Luschny at Fri Sep 09 04:19:39 EDT 2022
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#22 by Joerg Arndt at Fri Sep 09 04:03:35 EDT 2022
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#21 by Amiram Eldar at Fri Sep 09 03:29:43 EDT 2022
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#20 by Amiram Eldar at Fri Sep 09 02:51:53 EDT 2022
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| COMMENTS
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The numbers of terms not exceeding 10^k, for k = 4, 5, ..., are 1, 77, 473, 5703, 53569, 561610, 5525461, 54979537, ... . Apparently, the asymptotic density of this sequence exists and equals 0.0005... . - Amiram Eldar, Sep 09 2022
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| STATUS
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approved
editing
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#19 by Sean A. Irvine at Sun Jun 09 18:43:50 EDT 2019
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#18 by Michel Marcus at Sun Jun 09 12:57:48 EDT 2019
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#17 by Joerg Arndt at Sun Jun 09 11:56:12 EDT 2019
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#16 by Joerg Arndt at Sun Jun 09 11:56:09 EDT 2019
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| MATHEMATICA
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ExponentList[n_Integer, factors_List]:={#, IntegerExponent[n, # ]}&/@factors; InfinitaryDivisors[1]:={1}; InfinitaryDivisors[n_Integer?Positive]:=Module[ { factors=First/@FactorInteger[n], d=Divisors[n] }, d[[Flatten[Position[ Transpose[ Thread[Function[{f, g}, BitOr[f, g]==g][ #, Last[ # ]]]&/@ Transpose[Last/@ExponentList[ #, factors]&/@d]], _?(And@@#&), {1}]] ]] ] Null; properinfinitarydivisorsum[k_]:=Plus@@InfinitaryDivisors[k]-k; Select[Range[1, 50000, 2], properinfinitarydivisorsum[ # ]># &][ # ]># &] (* end of program *)
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proposed
editing
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#15 by Jinyuan Wang at Sun Jun 09 07:52:20 EDT 2019
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#14 by Jinyuan Wang at Sun Jun 09 07:51:13 EDT 2019
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| PROG
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(PARI) A049417(n) = {my(b, f=factorint(n)); prod(k=1, #f[, 2], b = binary(f[k, 2]); prod(j=1, #b, if(b[j], 1+f[k, 1]^(2^(#b-j)), 1)))}
isok(k) = A049417(k)>2*k&&k%2==1; \\ Jinyuan Wang, Jun 09 2019
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| STATUS
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reviewed
editing
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Discussion
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| Sun Jun 09
| 07:52
| Jinyuan Wang: could anyone finish some of my draft edits?
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