cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

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

Views

Author

Michel Marcus, Mar 11 2013

Keywords

Comments

Members of a sociable quadruple are usually listed in the order with which they appear in the corresponding aliquot sequence. Therefore, in a sociable quadruple the 1st member is abundant, and the 4th member is deficient. In all, we can get 4 possibilities, and a sociable quadruple can be (with A for abundant, and D for deficient) : AADD, ADDD, ADAD, AAAD. The numbers in these sequences have been voluntarily limited to 12 digits maximum, the current status of the exhaustive search (see Pedersen link).

Examples

			The first quadruple of this type is: 1264460, 1547860, 1727636, 1305184, that are respectively abundant, abundant, deficient, deficient.
		

Crossrefs

Extensions

a(21)-a(22) from Amiram Eldar, Apr 05 2024

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

Views

Author

Michel Marcus, Mar 11 2013

Keywords

Comments

See comments in A222975.

Examples

			The first quadruple of this type is: 4938136, 5753864, 5504056, 5423384, that are respectively abundant, deficient, deficient, deficient.
		

Crossrefs

Extensions

a(7)-a(8) from Amiram Eldar, Apr 05 2024

A222978 Smallest member of sociable quadruples with signature: abundant, abundant, abundant, deficient.

Original entry on oeis.org

330003580, 3705771825, 5373457070
Offset: 1

Views

Author

Michel Marcus, Mar 11 2013

Keywords

Comments

See comments in A222975.
a(4) > 10^14, if it exists. - Amiram Eldar, Apr 05 2024

Examples

			The first quadruple of this type is: 330003580, 363003980, 399304420, 440004764 that are respectively abundant, abundant, abundant, deficient.
		

Crossrefs

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

Views

Author

Michel Marcus, Jan 02 2014

Keywords

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.

Examples

			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->... .
		

Crossrefs

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;);}

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

Views

Author

Michel Marcus, Jan 02 2014

Keywords

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

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;);}
Showing 1-5 of 5 results.