A222975
Smallest member of sociable quadruples with signature: abundant, abundant, deficient, deficient.
Original entry on oeis.org
1264460, 2115324, 2784580, 7169104, 18656380, 28158165, 81128632, 174277820, 498215416, 1236402232, 1799281330, 2387776550, 2717495235, 2879697304, 15837081520, 17616303220, 91411869465, 111375706442, 661126361272, 741158497112, 1045805730255, 1092162882824
Offset: 1
The first quadruple of this type is: 1264460, 1547860, 1727636, 1305184, that are respectively abundant, abundant, deficient, deficient.
A222976
Smallest member of sociable quadruples with signature: abundant, deficient, deficient, deficient.
Original entry on oeis.org
4938136, 209524210, 4823923384, 8653956136, 21669628904, 44379752648, 3681459083984, 4553100850815
Offset: 1
The first quadruple of this type is: 4938136, 5753864, 5504056, 5423384, that are respectively abundant, deficient, deficient, deficient.
A222978
Smallest member of sociable quadruples with signature: abundant, abundant, abundant, deficient.
Original entry on oeis.org
330003580, 3705771825, 5373457070
Offset: 1
The first quadruple of this type is: 330003580, 363003980, 399304420, 440004764 that are respectively abundant, abundant, abundant, deficient.
A234969
Abundant numbers whose aliquot sequence is abundant, deficient, abundant, ..., etc.
Original entry on oeis.org
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
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->... .
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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;);}
A234970
Deficient numbers whose aliquot sequence is deficient, abundant, deficient, ..., etc.
Original entry on oeis.org
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
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->... .
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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;);}
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