A246281 - OEIS

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A246281

Numbers k for which A003961(k) < 2*k; Numbers n such that if n = product_{k >= 1} (p_k)^(c_k), then product_{k >= 1} (p_{k+1})^(c_k) < 2*n, where p_k indicates the k-th prime, A000040(k).

19

1, 2, 3, 5, 7, 11, 13, 17, 19, 22, 23, 25, 26, 29, 31, 33, 34, 37, 38, 41, 43, 46, 47, 51, 53, 55, 58, 59, 61, 62, 65, 67, 71, 73, 74, 77, 79, 82, 83, 85, 86, 87, 89, 93, 94, 95, 97, 101, 103, 106, 107, 109, 111, 113, 115, 118, 119, 121, 122, 123, 127, 129, 131, 133, 134, 137, 139

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Numbers n such that A003961(n) < 2*n.

Numbers n such that A048673(n) <= n.

All primes (A000040) are members. (Cf. Bertrand's postulate).

All terms are deficient (in A005100). See A286385. - Antti Karttunen, Aug 27 2020

LINKS

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

Wikipedia, Bertrand's postulate

Index entries for sequences computed from indices in prime factorization

EXAMPLE

1 is present, as 1 = empty product and 1 < 2.

2 = p_1 is in the sequence, as p_2 = 3 and 3/2 < 2.

4 = p_1 * p_1 is not a member, as p_2 * p_2 = 3*3 = 9, and 9/4 > 2.

22 = 2*11 = p_1 * p_5 is a member, as p_2 * p_6 = 39, and 39/22 < 2.

PROG

(PARI)

A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961

isA246281(n) = (A003961(n) < (n+n));

n = 0; i = 0; while(i < 10000, n++; if(isA246281(n), i++; write("b246281.txt", i, " ", n)));

(Scheme, with Antti Karttunen's IntSeq-library)

(define A246281 (MATCHING-POS 1 1 (lambda (n) (<= (A048673 n) n))))

CROSSREFS

Complement: A246282.

Union of A246351 and A048674.

Subsequence: A000040.

Subsequence of A005100.

Positions of zeros in A252742, in A336836, and in A337345.

Positions of negative terms in A252748.

Cf. A003961, A048673, A246361, A286385.

Sequence in context: A328513 A318719 A106317 * A369331 A152242 A166504

Adjacent sequences: A246278 A246279 A246280 * A246282 A246283 A246284

KEYWORD

nonn

AUTHOR

Antti Karttunen, Aug 24 2014

EXTENSIONS

A new shorter version of name prepended by Antti Karttunen, Aug 27 2020

STATUS

approved