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A246361 Numbers n such that if 2n-1 = product_{k >= 1} (p_k)^(c_k), then n >= product_{k >= 1} (p_{k-1})^(c_k), where p_k indicates the k-th prime, A000040(k).

%I A246361 #15 Aug 26 2014 01:27:13
%S A246361 1,2,3,5,8,11,13,14,17,18,23,25,26,28,32,33,38,39,41,43,50,53,58,59,
%T A246361 61,63,68,73,74,77,83,86,88,93,94,95,98,104,113,116,122,123,128,131,
%U A246361 137,138,140,143,149,158,163,167,172,173,176,179,182,185,188,193,194,200,203,212,213,215,218,221,228,230,233
%N A246361 Numbers n such that if 2n-1 = product_{k >= 1} (p_k)^(c_k), then n >= product_{k >= 1} (p_{k-1})^(c_k), where p_k indicates the k-th prime, A000040(k).
%C A246361 Numbers n such that A064216(n) <= n.
%C A246361 Numbers n such that A064989(2n-1) <= n.
%C A246361 The sequence grows as:
%C A246361       a(100) = 332
%C A246361      a(1000) = 3207
%C A246361     a(10000) = 34213
%C A246361    a(100000) = 340703
%C A246361   a(1000000) = 3388490
%C A246361 suggesting that overall, less than one third of natural numbers appear in this sequence, and more than two thirds in the complement, A246362. See also comments in the latter.
%H A246361 Antti Karttunen, <a href="/A246361/b246361.txt">Table of n, a(n) for n = 1..10000</a>
%e A246361 1 is present, as 2*1 - 1 = empty product = 1.
%e A246361 12 is not present, as (2*12)-1 = 23 = p_9, and p_8 = 19, with 12 < 19.
%e A246361 14 is present, as (2*14)-1 = 27 = p_2^3 = 8, and 14 >= 8.
%o A246361 (PARI)
%o A246361 default(primelimit, 2^30);
%o A246361 A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
%o A246361 A064216(n) = A064989((2*n)-1);
%o A246361 isA246361(n) = (A064216(n) <= n);
%o A246361 n = 0; i = 0; while(i < 10000, n++; if(isA246361(n), i++; write("b246361.txt", i, " ", n)));
%o A246361 (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o A246361 (define A246361 (MATCHING-POS 1 1 (lambda (n) (<= (A064216 n) n))))
%Y A246361 Complement: A246362.
%Y A246361 Union of A246371 and A048674.
%Y A246361 Subsequence: A246360.
%Y A246361 Cf. A000040, A064216, A064989, A246281.
%K A246361 nonn
%O A246361 1,2
%A A246361 _Antti Karttunen_, Aug 24 2014