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 A234969 Abundant numbers whose aliquot sequence is abundant, deficient, abundant, ..., etc. 1
 220, 1064, 1184, 2172, 2620, 5020, 6232, 10744, 12285, 17296, 63020, 66928, 67095, 69615, 79750, 80535, 83655, 86086, 100485, 122265, 122368, 141664, 142310, 146344, 171856, 173500, 176272, 177340, 185368, 191260, 196724, 280540, 308620, 319550, 333920 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS All smaller members of an amicable pair (A002025) belong to this sequence. Also abundant members of the sociable quadruple represented in A222977 are here. Starting at k=3, I found 1, 7, 18, 63, 160, 331, 858 terms up to 10^k. LINKS Table of n, a(n) for n=1..35. EXAMPLE The aliquot sequence 220->284->220->... has the requested form, so 220 is here. 1064 is here too since its aliquot sequence is 1064->1336->1184->1210->... . PROG (PARI) isAmicable(n)={my(a=sigma(n)-n); (a<>n) && (sigma(a)-a)==n; } \\ from A063990 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) && (ac) && (cb) && (bn)); } 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; ); } CROSSREFS Cf. A002025, A002046, A063990, A222977, A234970. Sequence in context: A258538 A257354 A102073 * A002025 A260086 A339678 Adjacent sequences: A234966 A234967 A234968 * A234970 A234971 A234972 KEYWORD nonn AUTHOR Michel Marcus, Jan 02 2014 STATUS approved

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Last modified April 22 08:12 EDT 2024. Contains 371893 sequences. (Running on oeis4.)