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

1,2

Comments

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.

Links

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

Example

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).

Prog

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

Crossrefs

Other than 1, indices of 1 in A356428.

Includes A000040 and A001358 as subsequences.

Complement of A356441.

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

Sequence in context: A330977 A188437 A344414 * A325456 A342524 A328161

Adjacent sequences: A356435 A356436 A356437 * A356439 A356440 A356441

Keyword

nonn,easy

Author

Jianing Song, Aug 07 2022

Status

approved