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Search: id:A157940
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| A157940 |
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Numbers n divisible by the largest prime <= sqrt(n) which are not in A001248 (primes squared) or A006094 (product of two consecutive primes). |
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3
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| 8, 12, 18, 24, 30, 40, 45, 56, 63, 70, 84, 98, 105, 112, 132, 154, 165, 182, 195, 208, 234, 260, 273, 286, 306, 340, 357, 380, 399, 418, 456, 475, 494, 513, 552, 575, 598, 621, 644, 690, 736, 759, 782, 805, 828, 870, 928, 957, 992, 1023, 1054, 1085, 1116, 1178
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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A subsequence of A157941.
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FORMULA
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A157940 = A157942 \ A157936 = A157941 \ A006094, where A157941 = A157942 \ A001248.
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EXAMPLE
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For numbers less than 4 the definition does not make sense, since there's no prime < 2=sqrt(4).
a(1)=8 which is divisible by 2 = precprime(sqrt(8)) and neither a prime squared (as would be 4 and 9) nor product of consecutive primes.
5 and 7 are not in this sequence, since not a multiple of 2=precprime(sqrt(5)) =precprime(sqrt(7)).
6 is not in the sequence, since it is the product of 2=precprime(sqrt(6)) and the following prime, 3. For the same reason, 15 is excluded.
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PROGRAM
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(PARI) for( n=5, 1999, n % precprime(sqrtint(n)) & next; n % nextprime(sqrtint(n-1)+1) & print1(n", "))
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CROSSREFS
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Sequence in context: A075818 A090738 A085103 this_sequence A087696 A015897 A028393
Adjacent sequences: A157937 A157938 A157939 this_sequence A157941 A157942 A157943
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KEYWORD
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nonn
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AUTHOR
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M. F. Hasler (MHasler(AT)univ-ag.fr), Mar 10 2009
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