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A246372 Numbers n such that 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). 12

%I

%S 1,2,3,4,6,7,9,10,12,15,16,19,20,21,22,24,25,26,27,29,30,31,33,34,35,

%T 36,37,40,42,44,45,46,47,48,49,51,52,54,55,56,57,60,62,64,65,66,67,69,

%U 70,71,72,75,76,78,79,80,81,82,84,85,87,89,90,91,92,93,96,97,99,100,101,102,103,105,106,107,108,109,110

%N Numbers n such that 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.

%H Antti Karttunen, <a href="/A246372/b246372.txt">Table of n, a(n) for n = 1..10000</a>

%e 1 is present, as 2*1 - 1 = empty product = 1.

%e 2 is present, as 2*2 - 1 = 3 = p_2, and p_{2-1} = p_1 = 2 >= 2.

%e 3 is present, as 2*3 - 1 = 5 = p_3, and p_{3-1} = p_2 = 3 >= 3.

%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 25 is present, as 2*25 - 1 = 49 = p_4^2, and p_3^2 = 5*5 = 25 >= 25.

%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 isA246372(n) = (A064216(n) >= n);

%o n = 0; i = 0; while(i < 10000, n++; if(isA246372(n), i++; write("b246372.txt", i, " ", n)));

%o (Scheme, with _Antti Karttunen_'s IntSeq-library)

%o (define A246372 (MATCHING-POS 1 1 (lambda (n) (>= (A064216 n) n))))

%Y Complement: A246371

%Y Union of A246362 and A048674.

%Y Subsequences: A006254 (A111333), A246373 (the primes present in this sequence).

%Y Cf. A000040, A064216, A064989, A246352.

%K nonn

%O 1,2

%A _Antti Karttunen_, Aug 24 2014

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Last modified January 25 16:42 EST 2020. Contains 331245 sequences. (Running on oeis4.)