A356441 -id:A356441 - cp's OEIS frontend

A356438 Numbers k such that A309892(k) = k/gpf(k), where gpf = A006530.

1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 19, 20, 21, 22, 23, 25, 26, 28, 29, 30, 31, 33, 34, 35, 37, 38, 39, 41, 42, 43, 44, 46, 47, 49, 51, 52, 53, 55, 56, 57, 58, 59, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 73, 74, 76, 77, 78, 79, 82, 83, 85

Offset: 1

Jianing Song, Aug 07 2022

Note that A309892(k) <= k/gpf(k); these sequence lists k such that the equality holds.

For k >= 2, k is a term if and only if k/gpf(k) < nextprime(gpf(k)), where nextprime = A151800.

			15 is a term since the number of steps needed to reach 0 of the iteration x -> x - gpf(x) starting at 15 is 3: 15 -> 10 -> 5 -> 0, and 3 = 15/gpf(15).

Jianing Song, Table of n, a(n) for n = 1..36902 (all terms <= 50000)

Other than 1, indices of 1 in A356428.
Includes A000040 and A001358 as subsequences.
Complement of A356441.
Cf. A309892, A006530 (gpf), A151800, A076563.

isA356438(n) = if(n>1, my(p=vecmax(factor(n)[, 1])); n/p

A356427 a(0) = 0, a(1) = 1; for n > 1, a(n) is the last step before reaching 0 of the iterations x -> x - gpf(x) starting at n, where gpf = A006530.

Original entry on oeis.org

0, 1, 2, 3, 2, 5, 3, 7, 3, 3, 5, 11, 3, 13, 7, 5, 7, 17, 5, 19, 5, 7, 11, 23, 7, 5, 13, 7, 7, 29, 5, 31, 5, 11, 17, 7, 11, 37, 19, 13, 7, 41, 7, 43, 11, 7, 23, 47, 7, 7, 7, 17, 13, 53, 17, 11, 7, 19, 29, 59, 11, 61, 31, 7, 31, 13, 11, 67, 17, 23, 7, 71, 23, 73, 37, 7, 19, 11

Offset: 0

Jianing Song, Aug 07 2022

nonn

For n > 1, a(n) is the unique prime in the iterations x -> x - gpf(x) starting at n and ending at 0.

			In the following examples the numbers produced by the iterations are listed together with their GPFs.
48 (3) -> 45 (5) -> 40 (5) -> 35 (7) -> ... -> 7 (7) -> 0, so a(48) = 7.
96 (3) -> 93 (31) -> 62 (31) -> 31 (31) -> 0, so a(96) = 31.

Jianing Song, Table of n, a(n) for n = 0..10000

Cf. A006530 (gpf), A076563, A309892, A356438, A356441.

a(n) = if(n>1, my(s=n); while(!isprime(s), s=s-vecmax(factor(s)[, 1])); s, n)

For n > 0, a(n) = gpf(n) if n is in A356438; otherwise a(n) > gpf(n).

cp's OEIS Frontend

A356438 Numbers k such that A309892(k) = k/gpf(k), where gpf = A006530.

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