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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).

%I A246281 #30 Apr 02 2025 15:18:17
%S A246281 1,2,3,5,7,11,13,17,19,22,23,25,26,29,31,33,34,37,38,41,43,46,47,51,
%T A246281 53,55,58,59,61,62,65,67,71,73,74,77,79,82,83,85,86,87,89,93,94,95,97,
%U A246281 101,103,106,107,109,111,113,115,118,119,121,122,123,127,129,131,133,134,137,139
%N 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).
%C A246281 Numbers n such that A003961(n) < 2*n.
%C A246281 Numbers n such that A048673(n) <= n.
%C A246281 All primes (A000040) are members. (Cf. Bertrand's postulate).
%C A246281 All terms are deficient (in A005100). See A286385. - _Antti Karttunen_, Aug 27 2020
%H A246281 Antti Karttunen, <a href="/A246281/b246281.txt">Table of n, a(n) for n = 1..10000</a>
%H A246281 Wikipedia, <a href="http://en.wikipedia.org/wiki/Bertrand%27s_postulate">Bertrand's postulate</a>
%H A246281 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%e A246281 1 is present, as 1 = empty product and 1 < 2.
%e A246281 2 = p_1 is in the sequence, as p_2 = 3 and 3/2 < 2.
%e A246281 4 = p_1 * p_1 is not a member, as p_2 * p_2 = 3*3 = 9, and 9/4 > 2.
%e A246281 22 = 2*11 = p_1 * p_5 is a member, as p_2 * p_6 = 39, and 39/22 < 2.
%o A246281 (PARI)
%o A246281 A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i,1] = nextprime(f[i,1]+1)); factorback(f);
%o A246281 isA246281(n) = (A003961(n) < (n+n));
%o A246281 n = 0; i = 0; while(i < 10000, n++; if(isA246281(n), i++; write("b246281.txt", i, " ", n)));
%o A246281 (Scheme)
%o A246281 ;; With _Antti Karttunen_'s IntSeq-library.
%o A246281 (define A246281 (MATCHING-POS 1 1 (lambda (n) (<= (A048673 n) n))))
%Y A246281 Complement: A246282.
%Y A246281 Union of A246351 and A048674.
%Y A246281 Subsequence: A000040.
%Y A246281 Subsequence of A005100.
%Y A246281 Positions of zeros in A252742, in A336836, and in A337345.
%Y A246281 Positions of negative terms in A252748.
%Y A246281 Cf. A003961, A048673, A246361, A286385.
%K A246281 nonn
%O A246281 1,2
%A A246281 _Antti Karttunen_, Aug 24 2014
%E A246281 A new shorter version of name prepended by _Antti Karttunen_, Aug 27 2020