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.

Previous Showing 11-17 of 17 results.

A186976 Number of ordered quintuples of distinct pairwise coprime positive integers with largest element n.

Original entry on oeis.org

2, 1, 3, 0, 26, 1, 72, 9, 14, 29, 228, 15, 431, 55, 115, 75, 928, 70, 743, 205, 633, 225, 2499, 70, 3571, 958, 1085, 728, 1626, 350, 6979, 1231, 2061, 822, 10800, 450, 13978, 2361, 2750, 2772, 20114, 1507, 15718, 2761, 7370, 4422, 33082, 2457, 13971
Offset: 7

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Author

Alois P. Heinz, Mar 01 2011

Keywords

Examples

			a(7) = 2 because there are 2 ordered quintuples of distinct pairwise coprime positive integers with largest element 7: (1,2,3,5,7), (1,3,4,5,7).

Links

Crossrefs

Column 5 of triangle A186972. First differences of A015698.

A186977 Number of ordered sextuples of distinct pairwise coprime positive integers with largest element n.

Original entry on oeis.org

6, 0, 33, 2, 3, 12, 157, 6, 400, 36, 76, 46, 1076, 56, 866, 186, 746, 216, 3880, 56, 6449, 1568, 1561, 1022, 2406, 448, 14767, 2023, 3465, 1260, 25860, 672, 37110, 4986, 5577, 5850, 58971, 3212, 45142, 6402, 18557, 10857, 110863, 6006, 39937
Offset: 11

Views

Author

Alois P. Heinz, Mar 02 2011

Keywords

Examples

			a(14) = 2 because there are 2 ordered sextuples of distinct pairwise coprime positive integers with largest element 14: (1,3,5,11,13,14), (1,5,9,11,13,14).

Links

Crossrefs

Column 6 of triangle A186972. First differences of A186982.

A186978 Number of ordered septuples of distinct pairwise coprime positive integers with largest element n.

Original entry on oeis.org

6, 0, 0, 2, 56, 1, 219, 13, 27, 15, 777, 28, 640, 102, 563, 127, 3923, 28, 7859, 1792, 1505, 966, 2354, 392, 21313, 2289, 3969, 1344, 42828, 714, 69360, 7566, 8118, 8826, 122883, 5082, 93084, 10890, 33594, 19338, 266024, 11011, 82350, 23298, 63917
Offset: 13

Views

Author

Alois P. Heinz, Mar 02 2011

Keywords

Examples

			a(16) = 2 because there are 2 ordered septuples of distinct pairwise coprime positive integers with largest element 16: (1,3,5,7,11,13,16), (1,5,7,9,11,13,16).

Links

Crossrefs

Column 7 of triangle A186972. First differences of A186983.

A186979 Number of ordered octuples of distinct pairwise coprime positive integers with largest element n.

Original entry on oeis.org

8, 0, 65, 2, 4, 2, 339, 8, 291, 31, 264, 42, 2576, 8, 6527, 1436, 967, 610, 1518, 232, 21395, 1793, 3123, 1002, 50310, 540, 93852, 8394, 8646, 9696, 187722, 6072, 141942, 13860, 44814, 25542, 472593, 15444, 126012, 33198, 96078, 60294, 959714
Offset: 17

Views

Author

Alois P. Heinz, Mar 02 2011

Keywords

Examples

			a(20) = 2 because there are 2 ordered octuples of distinct pairwise coprime positive integers with largest element 20: (1,3,7,11,13,17,19,20), (1,7,9,11,13,17,19,20).

Links

Crossrefs

Column 8 of triangle A186972. First differences of A186984.

A186980 Number of ordered 9-tuples of distinct pairwise coprime positive integers with largest element n.

Original entry on oeis.org

8, 0, 0, 0, 81, 1, 74, 4, 70, 6, 1056, 1, 3640, 793, 398, 247, 621, 89, 14930, 956, 1662, 513, 42243, 285, 93093, 6831, 6765, 7785, 213681, 5511, 162549, 13299, 44517, 25245, 633633, 16731, 145215, 36003, 108885, 67779, 1437252, 9867, 2406404
Offset: 19

Views

Author

Alois P. Heinz, Mar 02 2011

Keywords

Examples

			a(24) = 1 because there is one ordered 9-tuple of distinct pairwise coprime positive integers with largest element 24: (1,5,7,11,13,17,19,23,24).

Links

Crossrefs

Column 9 of triangle A186972. First differences of A186985.

A186981 Number of ordered 10-tuples of distinct pairwise coprime positive integers with largest element n.

Original entry on oeis.org

8, 0, 8, 0, 8, 0, 244, 0, 1301, 288, 95, 58, 146, 20, 7089, 331, 571, 172, 25150, 100, 67678, 4036, 3850, 4522, 182152, 3784, 140446, 9592, 32890, 18634, 646954, 14014, 126562, 29788, 93394, 57742, 1655200, 8008, 3102319, 253594, 261118, 505219
Offset: 23

Views

Author

Alois P. Heinz, Mar 02 2011

Keywords

Examples

			a(23) = 8 because there are 8 ordered 10-tuples of distinct pairwise coprime positive integers with largest element 23: (1,2,3,5,7,11,13,17,19,23), (1,2,5,7,9,11,13,17,19,23), (1,3,4,5,7,11,13,17,19,23), (1,3,5,7,8,11,13,17,19,23), (1,3,5,7,11,13,16,17,19,23), (1,4,5,7,9,11,13,17,19,23), (1,5,7,8,9,11,13,17,19,23), (1,5,7,9,11,13,16,17,19,23).

Links

Crossrefs

Column 10 of triangle A186972. First differences of A186986.

A319187 Number of pairwise coprime subsets of {1,...,n} of maximum cardinality (A036234).

Original entry on oeis.org

1, 1, 1, 2, 2, 2, 2, 3, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8, 16, 16, 24, 24, 24, 24, 24, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 72, 72, 72, 72, 72, 72, 72, 72
Offset: 1

Views

Author

Gus Wiseman, Jan 09 2019

Keywords

Comments

Two or more numbers are pairwise coprime if no pair of them has a common divisor > 1. A single number is not considered to be pairwise coprime unless it is equal to 1.

Examples

			The a(8) = 3 subsets are {1,2,3,5,7}, {1,3,4,5,7}, {1,3,5,7,8}.

Links

Crossrefs

Rightmost terms of A186974 and A320436.
Run lengths are A053707.
Cf. A015614, A036234, A051424, A085945, A186971, A186972, A186994, A276187, A303139, A320423, A320426.
Cf. A000005, A045948.

Programs

  • Mathematica
    Table[Length[Select[Subsets[Range[n],{PrimePi[n]+1}],CoprimeQ@@#&]],{n,24}] (* see A186974 for a faster program *)
  • PARI
    a(n) = prod(p=1, n, if (isprime(p), logint(n, p), 1)); \\ Michel Marcus, Dec 26 2020

Formula

a(n) = Product_{p prime <= n} floor(log_p(n)).
a(n) = A000005(A045948(n)). - Ridouane Oudra, Sep 02 2019
Previous Showing 11-17 of 17 results.

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