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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
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) && (a<b) && (b>c) && (c<n)) || ((n<a) && (a>b) && (b<c) && (c>n)); }
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
Sequence in context: A258538 A257354 A102073 * A002025 A260086 A339678
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.)