Search: id:A136446
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%I A136446
%S A136446 12,18,24,30,36,40,42,48,54,56,60,66,72,78,80,84,90,96,100,102,108,
%T A136446 112,114,120,126,132,138,140,144,150,156,160,162,168,174,176,180,
%U A136446 186,192,196,198,200,204,208,210,216,220,222,224,228,234,240,246
%N A136446 Numbers n such that some subset of the numbers { 1 < d < n : d divides 
               n } adds up to n.
%C A136446 The Eppstein link seems to say that there is a conjecture that there 
               is an odd number in the sequence, but no such number has yet been 
               found. - Joshua Zucker, Apr 08 2008
%C A136446 This is a subset of the pseudoperfect numbers A005835 and thus abundant 
               numbers A005101. Sequence A122036 lists odd abundant numbers (A005231) 
               which are not in this sequence. (As of today, no odd abundant number 
               is known which is not pseudoperfect.) - M. F. Hasler (www.univ-ag.fr/
               ~mhasler), Apr 13 2008
%C A136446 Values up to a(396) confirmed by R. J. Mathar. - M. F. Hasler (www.univ-ag.fr/
               ~mhasler), Apr 13 2008
%C A136446 This sequence contains infinitely many odd elements: any proper multiple 
               of any pseudoperfect number is in the sequence, so odd proper multiples 
               of odd pseudoperfect numbers are in the sequence. The first such 
               is 2835 = 3 * 945 (which is in the b-file). [From Franklin T. Adams-Watters 
               (FrankTAW(AT)Netscape.net), Jun 18 2009]
%H A136446 M. F. Hasler, <a href="b136446.txt">Table of n, a(n) for n=1,...,24491</
               a>.
%H A136446 David Eppstein, <a href="http://www.ics.uci.edu/~eppstein/numth/egypt/
               odd-one.html">Eqyptian Fractions</a>
%o A136446 (PARI/gp) N=72 \\ up to this value
%o A136446 vv=vector(N);
%o A136446 { for(n=2, N,
%o A136446 if ( isprime(n), next() );
%o A136446 d=divisors(n);
%o A136446 d=vector(#d-2,j,d[j+1]); \\ not n, not 1
%o A136446 for (k=1, (1<<#d)-1, \\ all subsets
%o A136446 t=vecextract(d, k);
%o A136446 if ( n==sum(j=1,#t,t[j]),
%o A136446 vv[n] += 1;););); }
%o A136446 for (j=1, #vv, if (vv[j]>0, print1(j,", "))) \\ A005835 (after correction)
%o A136446 (PARI code from M. F. Hasler, Apr 13 2008) /* this is equivalent to sigma(n)>
               2*n & isA005835(n,vecextract(divisors(n),"2..-2")) */
%o A136446 isA136446(n, d=0)={ local(t); if( !d, sigma(n)>2*n | return; d=vecextract(divisors(n),
               "2..-2"), setsearch( Set(d),n)&return(1)); while(#d>1&d[ #d ]>n,d=vecextract(d,
               "^-1")); n>=(t=sum(i=1,#d,d[ i ])) & return(n==t); n>d[ #d ] & isA136446(n-d[ 
               #d ],vecextract(d,"^-1")) & return(1); isA136446(n,vecextract(d,"^-1"))}
%o A136446 for( n=1,10^4, isA136446(n) & print1(n", "))
%Y A136446 See A005835 for another version with much more information.
%Y A136446 Cf. A122036 = A005231 \ A136446.
%Y A136446 Sequence in context: A107794 A162151 A056773 this_sequence A074726 A091013 
               A159886
%Y A136446 Adjacent sequences: A136443 A136444 A136445 this_sequence A136447 A136448 
               A136449
%K A136446 nonn
%O A136446 1,1
%A A136446 Joerg Arndt (arndt(AT)jjj.de), Apr 06 2008
%E A136446 More terms from M. F. Hasler, Apr 13 2008

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