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

Author

Michel Marcus, Jan 02 2014

Keywords

• nonn

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.

Examples

			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->... .
		

Crossrefs

Cf. A002025, A002046, A063990, A222977, A234969.

Programs

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;);}