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 A234970 Deficient numbers whose aliquot sequence is deficient, abundant, deficient, ..., etc. 1
 284, 1210, 1336, 2122, 2362, 2924, 5234, 5564, 6368, 10856, 12458, 13923, 14595, 18416, 34586, 36843, 66992, 71145, 74385, 76084, 80745, 85939, 87633, 88730, 89228, 90153, 91322, 91792, 123152, 124155, 139815, 153176, 156122, 163148, 168730, 171428, 172166 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS All larger members of an amicable pair (A002046) belong to this sequence. Also deficient members of the sociable quadruple represented in A222977 are here. Starting at k=3, I found 1, 9, 28, 93, 266, 774, 2821 terms up to 10^k. LINKS Table of n, a(n) for n=1..37. EXAMPLE The aliquot sequence 284->220->284->... has the requested form, so 284 is here. 2122 is here too, since its aliquot sequence is 2122->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, A234969. Sequence in context: A259996 A092681 A090789 * A260087 A002046 A339679 Adjacent sequences: A234967 A234968 A234969 * A234971 A234972 A234973 KEYWORD nonn AUTHOR Michel Marcus, Jan 02 2014 STATUS approved

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Last modified March 1 03:27 EST 2024. Contains 370430 sequences. (Running on oeis4.)