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

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

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) && (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, 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