A361321 -id:A361321 - cp's OEIS frontend

A361327 a(n) is the greatest prime factor of A361321(n) with a(1) = 1.

1, 3, 5, 7, 7, 11, 11, 7, 13, 13, 5, 11, 11, 7, 13, 13, 17, 17, 19, 19, 17, 17, 7, 5, 23, 23, 19, 19, 11, 23, 23, 13, 11, 29, 29, 7, 13, 31, 31, 23, 23, 37, 37, 11, 29, 29, 11, 41, 41, 31, 31, 13, 43, 43, 37, 37, 17, 47, 47, 53, 53, 59, 59, 61, 61, 13, 13, 67, 67, 71, 71, 73, 73, 79, 79, 11, 17

Offset: 1

Scott R. Shannon, Rémy Sigrist and N. J. A. Sloane, Mar 15 2023

nonn

			A361321(3) = 10 = 2*5, so a(3) = 5.

Scott R. Shannon, Table of n, a(n) for n = 1..10000

Cf. A361321, A000469, A361328 (least prime factor), A361329, A361329, A336957, A360519, A361120.

A361328 a(n) is the least prime factor of A361321(n) with a(1) = 1.

Original entry on oeis.org

1, 2, 2, 5, 3, 3, 2, 2, 7, 3, 3, 5, 7, 2, 2, 5, 5, 2, 2, 3, 3, 7, 2, 2, 3, 7, 7, 5, 2, 2, 13, 11, 2, 2, 5, 3, 2, 2, 5, 5, 2, 2, 5, 3, 3, 7, 2, 2, 3, 3, 7, 2, 2, 3, 3, 7, 2, 2, 3, 3, 2, 2, 3, 3, 2, 2, 3, 3, 2, 2, 3, 3, 2, 2, 3, 3, 11, 2, 2, 11, 11, 2, 2, 13, 13, 2, 2, 3, 3, 5, 7, 2, 2, 3, 5, 5

Offset: 1

Scott R. Shannon, Rémy Sigrist and N. J. A. Sloane, Mar 15 2023

nonn

			A361321(3) = 10 = 2*5, so a(3) = 2.

Scott R. Shannon, Table of n, a(n) for n = 1..10000

Cf. A361321, A000469, A361327 (greatest prime factor), A361329, A361329, A336957, A360519, A361119.

A361329 a(n) = gcd(A361321(n), A361321(n+1)).

Original entry on oeis.org

1, 2, 5, 7, 3, 11, 2, 7, 13, 3, 5, 11, 7, 2, 13, 5, 17, 2, 19, 3, 17, 7, 10, 3, 23, 7, 19, 5, 2, 23, 13, 11, 2, 29, 5, 3, 2, 31, 5, 23, 2, 37, 5, 3, 29, 7, 2, 41, 3, 31, 7, 2, 43, 3, 37, 7, 2, 47, 3, 53, 2, 59, 3, 61, 2, 65, 3, 67, 2, 71, 3, 73, 2, 79, 3, 11, 17, 2, 19, 11, 23, 2, 17, 13, 19, 2

Offset: 1

Scott R. Shannon, Rémy Sigrist and N. J. A. Sloane, Mar 15 2023

nonn

			A361321(3) = 10, A361321(4) = 35, so a(3) = gcd(10,35) = 5;

Scott R. Shannon, Table of n, a(n) for n = 1..10000

Cf. A361321, A000469, A361327, A361328, A361329, A336957, A360519, A361118.

A361323 a(n) = k such that A000469(k) = A361321(n).

Original entry on oeis.org

1, 2, 3, 12, 6, 10, 7, 4, 33, 14, 5, 18, 27, 15, 8, 22, 30, 11, 13, 19, 17, 45, 25, 9, 24, 62, 50, 36, 40, 16, 121, 55, 23, 20, 56, 38, 28, 21, 59, 43, 52, 26, 71, 63, 32, 79, 58, 29, 47, 34, 87, 69, 31, 48, 41, 105, 97, 35, 53, 61, 39, 44, 67, 70, 46, 49, 76, 77, 51, 54, 84, 89, 57, 60, 96

Offset: 1

Scott R. Shannon, Rémy Sigrist, and N. J. A. Sloane, Mar 11 2023

nonn

Conjectured to be a permutation of the natural numbers (if not then there exists a k such that A000469(k) does not appear in A361321).

Scott R. Shannon, Table of n, a(n) for n = 1..10000.

Cf. A361321, A000469, A361324, A336957, A360519, A361102.

A361324 a(n) = k such that A361321(k) = A000469(n), or -1 if A000469(n) never appears in A361321.

Original entry on oeis.org

1, 2, 3, 8, 11, 5, 7, 15, 24, 6, 18, 4, 19, 10, 14, 30, 21, 12, 20, 34, 38, 16, 33, 25, 23, 42, 13, 37, 48, 17, 53, 45, 9, 50, 58, 28, 83, 36, 61, 29, 55, 79, 40, 62, 22, 65, 49, 54, 66, 27, 69, 41, 59, 70, 32, 35, 73, 47, 39, 74, 60, 26, 44, 87, 78, 93, 63, 98, 52, 64, 43, 101, 77, 86, 102

Offset: 1

Scott R. Shannon, Rémy Sigrist, and N. J. A. Sloane, Mar 11 2023

nonn

Conjectured to be a permutation of the natural numbers (and if so, -1 will never appear).

Scott R. Shannon, Table of n, a(n) for n = 1..10000.

Cf. A361321, A000469, A361323, A336957, A360519, A361102.

A361322 The binary expansion of a(n) specifies which primes divide A361321(n).

Original entry on oeis.org

0, 3, 5, 12, 10, 18, 17, 9, 40, 34, 6, 20, 24, 11, 33, 36, 68, 65, 129, 130, 66, 72, 13, 7, 258, 264, 136, 132, 21, 257, 288, 48, 19, 513, 516, 14, 35, 1025, 1028, 260, 259, 2049, 2052, 22, 514, 520, 25, 4097, 4098, 1026, 1032, 41, 8193, 8194, 2050, 2056, 73

Offset: 1

Scott R. Shannon, Rémy Sigrist and N. J. A. Sloane, Mar 09 2023

Conjecture: The sequence is a permutation of A057716.

Rémy Sigrist, PARI program

Cf. A057716, A087207, A361321.

PARI
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a(n) = A087207(A360519(n)).

A361325 Records in A361321.

Original entry on oeis.org

1, 6, 10, 35, 91, 119, 161, 299, 445, 623, 1067, 1351, 1379, 1561, 1589, 1603, 1631, 2051, 2681, 3199, 3829, 4207, 4963, 5089, 6139, 7427, 7441, 8953, 15037, 21769, 26389, 35519, 42647, 49423, 53471, 70279, 77297, 95843, 102839, 111661, 116677, 146707, 158059, 172051, 181247, 206503, 227491

Offset: 1

Scott R. Shannon, Rémy Sigrist and N. J. A. Sloane, Mar 11 2023

nonn

Cf. A361321, A000469, A361326, A360519, A361107.

A361326 Indices of records in A361321.

Original entry on oeis.org

1, 2, 3, 4, 9, 22, 26, 31, 95, 99, 132, 216, 222, 287, 293, 298, 303, 321, 406, 490, 581, 643, 764, 791, 932, 1131, 1138, 1346, 1439, 2077, 2541, 3434, 4123, 4813, 5216, 6883, 7525, 9404, 10107, 10975, 11457, 14462, 15565, 16977, 17908, 20456, 22557, 22779, 23929, 29033, 35776, 38811, 43493

Offset: 1

Scott R. Shannon, Rémy Sigrist and N. J. A. Sloane, Mar 11 2023

nonn

Cf. A361321, A000469, A361325, A360519, A361107.

cp's OEIS Frontend

A361327 a(n) is the greatest prime factor of A361321(n) with a(1) = 1.

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A361328 a(n) is the least prime factor of A361321(n) with a(1) = 1.

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A361329 a(n) = gcd(A361321(n), A361321(n+1)).

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A361323 a(n) = k such that A000469(k) = A361321(n).

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A361324 a(n) = k such that A361321(k) = A000469(n), or -1 if A000469(n) never appears in A361321.

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A361322 The binary expansion of a(n) specifies which primes divide A361321(n).

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A361325 Records in A361321.

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A361326 Indices of records in A361321.

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