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%I #17 Aug 26 2014 01:27:28
%S 4,6,7,9,10,12,15,16,19,20,21,22,24,27,29,30,31,34,35,36,37,40,42,44,
%T 45,46,47,48,49,51,52,54,55,56,57,60,62,64,65,66,67,69,70,71,72,75,76,
%U 78,79,80,81,82,84,85,87,89,90,91,92,96,97,99,100,101,102,103,105,106,107,108,109,110,111,112,114,115
%N 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 Numbers n such that A064216(n) > n.
%C Numbers n such that A064989(2n-1) > n.
%C The sequence grows as:
%C a(100) = 148
%C a(1000) = 1449
%C a(10000) = 14264
%C a(100000) = 141259
%C a(1000000) = 1418197
%C and the powers of 10 occur at:
%C a(5) = 10
%C a(63) = 100
%C a(701) = 1000
%C a(6973) = 10000
%C a(70845) = 100000
%C a(705313) = 1000000
%C suggesting that the ratio a(n)/n is converging to a constant and an arbitrary natural number is more than twice as likely to be here than in the complement A246361. Compare this to the ratio present in the "inverse" case A246282.
%H Antti Karttunen, <a href="/A246362/b246362.txt">Table of n, a(n) for n = 1..10000</a>
%e 4 is present, as 2*4 - 1 = 7 = p_4, and p_{4-1} = p_3 = 5 > 4.
%e 5 is not present, as 2*5 - 1 = 9 = p_2 * p_2, and p_1 * p_1 = 4, with 4 < 5.
%e 6 is present, as 2*6 - 1 = 11 = p_5, and p_{5-1} = p_4 = 7 > 6.
%e 35 is present, as 2*35 - 1 = 69 = 3*23 = p_2 * p_9, and p_1 * p_8 = 2*19 = 38 > 35.
%o (PARI)
%o default(primelimit, 2^30);
%o 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 A064216(n) = A064989((2*n)-1);
%o isA246362(n) = (A064216(n) > n);
%o n = 0; i = 0; while(i < 10000, n++; if(isA246362(n), i++; write("b246362.txt", i, " ", n)));
%o (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o (define A246362 (MATCHING-POS 1 1 (lambda (n) (> (A064216 n) n))))
%Y Complement: A246361.
%Y Setwise difference of A246372 and A048674.
%Y Cf. A000040, A064216, A064989, A246282.
%K nonn
%O 1,1
%A _Antti Karttunen_, Aug 24 2014
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