A356438 -id:A356438 - cp's OEIS frontend

A356441 Numbers k such that A309892(k) < k/gpf(k), where gpf = A006530; complement of A356438.

8, 16, 18, 24, 27, 32, 36, 40, 45, 48, 50, 54, 60, 64, 72, 75, 80, 81, 84, 90, 96, 98, 100, 105, 108, 112, 120, 125, 126, 128, 135, 140, 144, 147, 150, 154, 160, 162, 165, 168, 175, 176, 180, 189, 192, 196, 198, 200, 210, 216, 220, 224, 225, 231, 234, 240, 242, 243

Offset: 1

Jianing Song, Aug 07 2022

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

			8 is a term since the number of steps needed to reach 0 of the iteration x -> x - gpf(x) starting at 8 is 3: 8 -> 6 -> 3 -> 0, and 3 < 8/gpf(8).

Jianing Song, Table of n, a(n) for n = 1..13098 (all terms <= 50000)

Cf. A356438, A309892, A006530 (gpf), A151800, A076563.

isA356441(n) = if(n>1, my(p=vecmax(factor(n)[, 1])); n/p>nextprime(p+1), 0)

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

A356441 Numbers k such that A309892(k) < k/gpf(k), where gpf = A006530; complement of A356438.

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