A337612 -id:A337612 - cp's OEIS frontend

A337609 Positive integers m such that A126286^k(m) = m for some positive integer k.

2, 3, 14, 21, 26, 34, 38, 39, 50, 57, 62, 74, 75, 85, 86, 93, 94, 98, 110, 111, 118, 122, 129, 134, 142, 146, 147, 154, 158, 165, 170, 182, 183, 194, 201, 202, 206, 214, 218, 219, 230, 235, 237, 242, 254, 255, 266, 273, 274, 278, 286, 290, 291, 298, 302, 309

Offset: 1

Ely Golden, Oct 07 2020

A126286^k(m) means apply A126286 to m k times.
Equivalently, the numbers that belong to a cycle under the map x -> A126286(x).
For any term m in this sequence, A126286(A126286(m)) = m.
Supersequence of A017545. Moreover, this sequence can be represented as an infinite union of arithmetic progressions.
2 and 3 are the only primes in this sequence.

			3 is a term since A126286(A126286(3)) = A126286(2) = 3.

Ely Golden, Table of n, a(n) for n = 1..10000
Ely Golden, Python program for generating terms of this sequence

Cf. A017545, A126286, A337610, A337611, A337612.

A337610 Positive integers m such that A126287^k(m) = m for some positive integer k.

Original entry on oeis.org

1, 10, 15, 22, 26, 33, 34, 46, 51, 58, 65, 69, 70, 82, 86, 87, 94, 105, 106, 118, 122, 123, 130, 134, 141, 142, 146, 154, 159, 166, 177, 178, 190, 195, 202, 206, 213, 214, 215, 218, 226, 231, 238, 249, 250, 254, 262, 266, 267, 274, 285, 286, 298, 302, 303, 310

Offset: 1

Ely Golden, Oct 07 2020

A126287^k(m) means apply A126287 to m k times.
Equivalently, the numbers that belong to a cycle under the map x -> A126287(x).
For any term m in this sequence, A126287(A126287(m)) = m.
Supersequence of A017641. Moreover, this sequence (excluding the first term) can be represented as an infinite union of arithmetic progressions.
There are no primes in this sequence.

			10 is a term since A126287(A126287(10)) = A126287(15) = 10.

Ely Golden, Table of n, a(n) for n = 1..10000
Ely Golden, Python program for generating terms of this sequence

Cf. A017641, A126287, A337609, A337611, A337612.

A337611 Positive integers m such that A126288^k(m) = m for some positive integer k.

Original entry on oeis.org

2, 3, 6, 10, 14, 20, 22, 26, 28, 38, 44, 46, 52, 76, 78, 88, 94, 102, 105, 114, 116, 117, 136, 138, 152, 171, 186, 187, 195, 207, 212, 247, 248, 266, 282, 284, 285, 296, 304, 322, 333, 354, 366, 369, 387, 402, 403, 407, 414, 423, 425, 426, 430, 437, 442, 468

Offset: 1

Ely Golden, Sep 05 2020

nonn

A126288^k(m) means apply A126288 to m k times.
Equivalently, the numbers that belong to a cycle under the map x -> A126288(x).
2 and 3 are the only primes in this sequence.

			3 is a term since A126288(A126288(3)) = A126288(2) = 3.

Ely Golden, Table of n, a(n) for n = 1..7144
Ely Golden, Python program for (naïvely) generating terms of this sequence

Cf. A337609, A337610, A337612, A126288, A052126.

gpf(n) = vecmax(factor(n)[,1]);
f(n) = if (n==1, 2, n*gpf(n+1)/gpf(n)); \\ A126288
incycle(n, list) = {my(v=Vec(list)); #select(x->(x==n), v);}
cycle(n) = {my(list = List(), repeat=1); while(repeat, n = f(n); if (incycle(n, list), repeat=0); listput(list, n);); list;}
isok(n) = {my(list = cycle(n)); incycle(n, list);} \\ Michel Marcus, Sep 08 2020

For any term m, gcd {m, A126288(m), A126288(A126288(m)), ...} = A052126(m).

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A337609 Positive integers m such that A126286^k(m) = m for some positive integer k.

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A337610 Positive integers m such that A126287^k(m) = m for some positive integer k.

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A337611 Positive integers m such that A126288^k(m) = m for some positive integer k.

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