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A158942
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Nonsquares coprime to 10.
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1
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3, 7, 11, 13, 17, 19, 21, 23, 27, 29, 31, 33, 37, 39, 41, 43, 47, 51, 53, 57, 59, 61, 63, 67, 69, 71, 73, 77, 79, 83, 87, 89, 91, 93, 97, 99, 101, 103, 107, 109, 111, 113, 117, 119, 123, 127, 129, 131, 133, 137, 139, 141, 143, 147, 149, 151, 153, 157, 159, 161, 163
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OFFSET
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1,1
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COMMENTS
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Odd primes + odd nonprime integers that have an odd numbers of proper divisors A082686, are the result of a suppression of integers satisfying: 2n (A005843); n^2 (A000290); n^2+n (A002378). Of these, we can suppress the multiples of 5 (A008587).
Decimal expansion of 1/10^(n^2+n) + 1/10^(n^2) + 1/10^(5*n) + 1/10^(2*n) gives a 0 for these integers.
2n + n(n+1) + n^2 = 2n^2 + 3n = A014106.
2n^2 + 3n + 5n = 2n^2 + 8n = 2n(n+4) = A067728 8(8+n) is a perfect square.
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LINKS
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MATHEMATICA
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Select[Range@ 163, ! IntegerQ@ Sqrt@ # && CoprimeQ[#, 10] &] (* Michael De Vlieger, Dec 11 2015 *)
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PROG
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(PARI) isok(n) = (n % 2) && (n % 5) && (isprime(n) || (numdiv(n) % 2 == 0)); \\ Michel Marcus, Aug 27 2013
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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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EXTENSIONS
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STATUS
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approved
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