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A234970 Deficient numbers whose aliquot sequence is deficient, abundant, deficient, ..., etc. 1

%I #10 Jan 05 2014 05:15:46

%S 284,1210,1336,2122,2362,2924,5234,5564,6368,10856,12458,13923,14595,

%T 18416,34586,36843,66992,71145,74385,76084,80745,85939,87633,88730,

%U 89228,90153,91322,91792,123152,124155,139815,153176,156122,163148,168730,171428,172166

%N Deficient numbers whose aliquot sequence is deficient, abundant, deficient, ..., etc.

%C All larger members of an amicable pair (A002046) belong to this sequence.

%C Also deficient members of the sociable quadruple represented in A222977 are here.

%C Starting at k=3, I found 1, 9, 28, 93, 266, 774, 2821 terms up to 10^k.

%e The aliquot sequence 284->220->284->... has the requested form, so 284 is here.

%e 2122 is here too, since its aliquot sequence is 2122->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, A234969.

%K nonn

%O 1,1

%A _Michel Marcus_, Jan 02 2014

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Last modified April 21 10:39 EDT 2024. Contains 371852 sequences. (Running on oeis4.)