

A246372


Numbers n such that 2n1 = product_{k >= 1} (p_k)^(c_k), then n <= product_{k >= 1} (p_{k1})^(c_k), where p_k indicates the kth 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
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OFFSET

1,2


COMMENTS

Numbers n such that A064216(n) >= n.
Numbers n such that A064989(2n1) >= 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_{21} = p_1 = 2 >= 2.
3 is present, as 2*3  1 = 5 = p_3, and p_{31} = 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_{51} = 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 IntSeqlibrary)
(define A246372 (MATCHINGPOS 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



