A234969 Abundant numbers whose aliquot sequence is abundant, deficient, abundant, ..., etc.

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

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) && (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

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