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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
 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, 36, 37, 40, 42, 44, 45, 46, 47, 48, 49, 51, 52, 54, 55, 56, 57, 60, 62, 64, 65, 66, 67, 69, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Numbers n such that A064216(n) >= n. Numbers n such that A064989(2n-1) >= n. LINKS Antti Karttunen, Table of n, a(n) for n = 1..10000 EXAMPLE 1 is present, as 2*1 - 1 = empty product = 1. 2 is present, as 2*2 - 1 = 3 = p_2, and p_{2-1} = p_1 = 2 >= 2. 3 is present, as 2*3 - 1 = 5 = p_3, and p_{3-1} = p_2 = 3 >= 3. 5 is not present, as 2*5 - 1 = 9 = p_2 * p_2, and p_1 * p_1 = 4, with 4 < 5. 6 is present, as 2*6 - 1 = 11 = p_5, and p_{5-1} = p_4 = 7 >= 6. 25 is present, as 2*25 - 1 = 49 = p_4^2, and p_3^2 = 5*5 = 25 >= 25. 35 is present, as 2*35 - 1 = 69 = 3*23 = p_2 * p_9, and p_1 * p_8 = 2*19 = 38 >= 35. PROG (PARI) default(primelimit, 2^30); 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)}; A064216(n) = A064989((2*n)-1); isA246372(n) = (A064216(n) >= n); n = 0; i = 0; while(i < 10000, n++; if(isA246372(n), i++; write("b246372.txt", i, " ", n))); (Scheme, with Antti Karttunen's IntSeq-library) (define A246372 (MATCHING-POS 1 1 (lambda (n) (>= (A064216 n) n)))) CROSSREFS Complement: A246371 Union of A246362 and A048674. Subsequences: A006254 (A111333), A246373 (the primes present in this sequence). Cf. A000040, A064216, A064989, A246352. Sequence in context: A171511 A225819 A205805 * A006254 A111333 A047701 Adjacent sequences:  A246369 A246370 A246371 * A246373 A246374 A246375 KEYWORD nonn AUTHOR Antti Karttunen, Aug 24 2014 STATUS approved

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Last modified September 26 15:53 EDT 2021. Contains 347668 sequences. (Running on oeis4.)