A277334 Numbers n, that apart from 2 are all odd and for which n/(largest prime dividing n) is squarefree.

1, 2, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 29, 31, 33, 35, 37, 39, 41, 43, 47, 49, 51, 53, 55, 57, 59, 61, 65, 67, 69, 71, 73, 75, 77, 79, 83, 85, 87, 89, 91, 93, 95, 97, 101, 103, 105, 107, 109, 111, 113, 115, 119, 121, 123, 127, 129, 131, 133, 137, 139, 141, 143, 145, 147, 149, 151, 155, 157, 159, 161, 163, 165, 167, 169

Offset

1,2

Comments

In other words, after 1 and 2, such odd numbers that only the largest prime factor in their prime factorization may have exponent 1 or 2, while all lesser prime factors occur at most once.

Links

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

Maple

with(numtheory): A277334_list := n -> seq(`if`(i=2 or (i::odd and issqrfree(i/ max(factorset(i)))), i, NULL), i=1..n): A277334_list(169); # Peter Luschny, Oct 23 2016

Prog

(Scheme, with Antti Karttunen's IntSeq-library)
(define A277334 (MATCHING-POS 1 1  (lambda (n) (and (or (= 2 n) (not (even? n))) (not (zero? (A008683 (A052126 n))))))))

Crossrefs

Disjoint union of A056911 and A129598(A056911(n)).

Cf. A005117, A008683, A052126.

Cf. A277332 (permutation of this sequence).

Differs from A091377 for the first time at n=36, where a(36)=75, while A091377(36)=77.

Sequence in context: A004274 A004280 A053224 * A091377 A336119 A213511

Adjacent sequences: A277331 A277332 A277333 * A277335 A277336 A277337

Keyword

nonn

Author

Antti Karttunen, Oct 12 2016

Status

approved