1,1

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

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

Values up to a(396) confirmed by R. J. Mathar. - M. F. Hasler (www.univ-ag.fr/~mhasler), Apr 13 2008

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]

M. F. Hasler, Table of n, a(n) for n=1,...,24491.

David Eppstein, Eqyptian Fractions

(PARI/gp) N=72 \\ up to this value

vv=vector(N);

{ for(n=2, N,

if ( isprime(n), next() );

d=divisors(n);

d=vector(#d-2, j, d[j+1]); \\ not n, not 1

for (k=1, (1<<#d)-1, \\ all subsets

t=vecextract(d, k);

if ( n==sum(j=1, #t, t[j]),

vv[n] += 1; ); ); ); }

for (j=1, #vv, if (vv[j]>0, print1(j, ", "))) \\ A005835 (after correction)

(PARI code from M. F. Hasler, Apr 13 2008) /* this is equivalent to sigma(n)>2*n & isA005835(n, vecextract(divisors(n), "2..-2")) */

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"))}

for( n=1, 10^4, isA136446(n) & print1(n", "))

See A005835 for another version with much more information.

Cf. A122036 = A005231 \ A136446.

Adjacent sequences: A136443 A136444 A136445 this_sequence A136447 A136448 A136449

Sequence in context: A107794 A162151 A056773 this_sequence A074726 A091013 A159886

nonn

Joerg Arndt (arndt(AT)jjj.de), Apr 06 2008

More terms from M. F. Hasler, Apr 13 2008