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%I #12 Jan 05 2014 05:15:29
%S 220,1064,1184,2172,2620,5020,6232,10744,12285,17296,63020,66928,
%T 67095,69615,79750,80535,83655,86086,100485,122265,122368,141664,
%U 142310,146344,171856,173500,176272,177340,185368,191260,196724,280540,308620,319550,333920
%N Abundant numbers whose aliquot sequence is abundant, deficient, abundant, ..., etc.
%C All smaller members of an amicable pair (A002025) belong to this sequence.
%C Also abundant members of the sociable quadruple represented in A222977 are here.
%C Starting at k=3, I found 1, 7, 18, 63, 160, 331, 858 terms up to 10^k.
%e The aliquot sequence 220->284->220->... has the requested form, so 220 is here.
%e 1064 is here too since its aliquot sequence is 1064->1336->1184->1210->... .
%o (PARI) isAmicable(n)={my(a=sigma(n)-n); (a<>n) && (sigma(a)-a)==n;} \\ from A063990
%o isSociableADAD(n)={my(a=sigma(n)-n); if (!a, return (0)); my(b=sigma(a)-a); if(! b, return (0)); my(c=sigma(b)-b); if (!c, return (0)); my(d=sigma(c)-c); if (d != n, return (0)); ((n>a) && (a<b) && (b>c) && (c<n)) || ((n<a) && (a>b) && (b<c) && (c>n));}
%o isok(n) = {my(oldn = n); my(newn = sigma(oldn) - oldn); my(dir = sign(newn - oldn)); if (!dir || (dir < 0), return (0)); oldn = newn; while (1, newn = sigma(oldn) - oldn; ndir = sign(newn - oldn); if (!ndir || (ndir == dir), return (0)); if (isAmicable(oldn), return(1)); if (isSociableADAD(oldn), return(1)); oldn = newn; dir = ndir;);}
%Y Cf. A002025, A002046, A063990, A222977, A234970.
%K nonn
%O 1,1
%A _Michel Marcus_, Jan 02 2014
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