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A276378
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Numbers k such that 6*k is squarefree.
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13
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1, 5, 7, 11, 13, 17, 19, 23, 29, 31, 35, 37, 41, 43, 47, 53, 55, 59, 61, 65, 67, 71, 73, 77, 79, 83, 85, 89, 91, 95, 97, 101, 103, 107, 109, 113, 115, 119, 127, 131, 133, 137, 139, 143, 145, 149, 151, 155, 157, 161, 163, 167, 173, 179, 181, 185, 187, 191, 193, 197, 199, 203, 205, 209, 211
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OFFSET
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1,2
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COMMENTS
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These are the numbers from A005117 that are not divisible by 2 and 3.
The products generated from each subset of A215848 (primes greater than 3).
Closed under the commutative binary operation A059897(.,.), forming a subgroup of the positive integers under A059897. (End)
Multiplied by 6 we have 6, 30, 42, 66, 78, 102, ..., the values that may appear in A076978 after the 1, 2. [Don Reble, Dec 02 2020] - R. J. Mathar, Dec 15 2020
By the von Staudt-Clausen theorem, denominators of Bernoulli numbers are of the form 6*a(n) for some n. - Charles R Greathouse IV, May 16 2024
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LINKS
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FORMULA
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Sum_{n>=1} 1/a(n)^s = (6^s)*zeta(s)/((1+2^s)*(1+3^s)*zeta(2*s)), s>1. - Amiram Eldar, Sep 26 2023
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EXAMPLE
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5 is in this sequence because 6*5 = 30 = 2*3*5 is squarefree.
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MAPLE
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select(numtheory:-issqrfree, [seq(seq(6*i+j, j=[1, 5]), i=0..100)]); # Robert Israel, Sep 02 2016
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MATHEMATICA
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PROG
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(Magma) [n: n in [1..230] | IsSquarefree(6*n)];
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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