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).

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

Offset: 1

Author

Antti Karttunen, Aug 24 2014

Keywords

• nonn

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

Examples

			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.
		

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

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.

Programs

PARI

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

Extensions

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