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A374277
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Numbers k divisible by exactly one of the prime factors of 30.
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1
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2, 3, 4, 5, 8, 9, 14, 16, 21, 22, 25, 26, 27, 28, 32, 33, 34, 35, 38, 39, 44, 46, 51, 52, 55, 56, 57, 58, 62, 63, 64, 65, 68, 69, 74, 76, 81, 82, 85, 86, 87, 88, 92, 93, 94, 95, 98, 99, 104, 106, 111, 112, 115, 116, 117, 118, 122, 123, 124, 125, 128, 129, 134
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OFFSET
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1,1
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COMMENTS
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Numbers k congruent to r (mod 30), where r is in {2, 3, 4, 5, 8, 9, 14, 16, 21, 22, 25, 26, 27, 28}, residues r = p^m mod 30 and r = (30 - p^m) mod 30.
The asymptotic density of this sequence is 7/15. - Amiram Eldar, Jul 26 2024
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,0,0,0,1,-1).
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FORMULA
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Intersection of this sequence and 5-smooth numbers (A051037) is A306044 \ {1}.
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EXAMPLE
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8 is in this sequence since it is even and a multiple of neither 3 nor 5.
10 is not in this sequence since 10 = 2*5; both 2 and 5 divide 30.
14 is in this sequence since it is even and a multiple of neither 3 nor 5, etc.
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MATHEMATICA
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s = Prime@ Range[3]; k = Times @@ s; r = Union[#, k - #] &@ Flatten@ Map[PowerRange[#, k, #] &, s]; m = Length[r]; Array[k*#1 + r[[1 + #2]] & @@ QuotientRemainder[# - 1, m] &, 60]
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PROG
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(PARI) is(k) = isprime(gcd(k, 30)); \\ Amiram Eldar, Jul 26 2024
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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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