A251727 Numbers n > 1 for which gpf(n) > spf(n)^2, where spf and gpf (smallest and greatest prime factor of n) are given by A020639(n) and A006530(n).

10, 14, 20, 22, 26, 28, 30, 33, 34, 38, 39, 40, 42, 44, 46, 50, 51, 52, 56, 57, 58, 60, 62, 66, 68, 69, 70, 74, 76, 78, 80, 82, 84, 86, 87, 88, 90, 92, 93, 94, 98, 99, 100, 102, 104, 106, 110, 111, 112, 114, 116, 117, 118, 120, 122, 123, 124, 126, 129, 130, 132, 134, 136, 138, 140, 141, 142, 145, 146, 148, 150, 152

Offset

1,1

Comments

Numbers n > 1 for which the smallest r such that r^k <= spf(n) and gpf(n) < r^(k+1) [for some k >= 0] is gpf(n)+1. Here spf and gpf (smallest and greatest prime factor of n) are given by A020639(n) and A006530(n). (The original, equivalent definition of the sequence).

Numbers n > 1 such that A252375(n) = 1 + A006530(n). Equally, one can substitute A251725 for A252375.

Numbers n > 1 for which there doesn't exist any r <= gpf(n) such that r^k <= spf(n) and gpf(n) < r^(k+1), for some k >= 0, where spf and gpf (smallest and greatest prime factor of n) are given by A020639(n) and A006530(n).

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Prog

(Scheme with Antti Karttunen's IntSeq-library, three alternative versions)
(define A251727 (MATCHING-POS 1 2 (lambda (n) (> (A006530 n) (A000290 (A020639 n))))))
(define A251727 (MATCHING-POS 1 2 (lambda (n) (= (A251725 n) (+ 1 (A006530 n))))))
(define A251727 (MATCHING-POS 1 2 (lambda (n) (= (A252375 n) (+ 1 (A006530 n))))))

Crossrefs

Complement: A251726. Subsequence: A138511.

Gives the positions of zeros in A252374 following its initial term.

Cf. A252371 (difference between the prime indices of gpf and spf of each a(n)).

Cf. A006530, A020639, A252375, A251725.

Related permutations: A252757-A252758.

Sequence in context: A162685 A272374 A362982 * A253785 A245729 A031274

Adjacent sequences: A251724 A251725 A251726 * A251728 A251729 A251730

Keyword

nonn

Author

Antti Karttunen, Dec 17 2014. A new simpler definition found Jan 01 2015 and the original definition moved to the Comments section

Status

approved