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A095738
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Numbers that are coprime to sigma but are not prime powers.
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5
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21, 35, 36, 39, 50, 55, 57, 63, 65, 75, 77, 85, 93, 98, 100, 111, 115, 119, 129, 133, 143, 144, 155, 161, 171, 175, 183, 185, 187, 189, 201, 203, 205, 209, 215, 217, 219, 221, 225, 235, 237, 242, 245, 247, 253, 259, 265, 275, 279, 291, 299, 301, 305, 309, 319
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OFFSET
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1,1
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COMMENTS
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Abundancy is defined as the ratio of the multiplicative sum-of-divisors function to the integer itself: abund(n) = sigma(n)/n. E.g., abund(10) = sigma(10) / 10 = (1+2+5+10) / 10 = 1.8 = 9 / 5.
Integers m and n are friendly if and only if they have the same abundancy. E.g., abund(12) = abund(234) = 7 / 3, so 12 and 234 are friends.
Integers which have no friends are called solitary.
The numbers in this sequence are solitary.
Compare abundancy to abundance as defined in A033880.
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LINKS
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MATHEMATICA
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Select[Range[320], PrimeNu[#] > 1 && GCD[#, DivisorSigma[1, #]] == 1 &] (* Amiram Eldar, Jun 25 2019 *)
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PROG
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(PARI) isok(n) = (gcd(sigma(n), n) == 1) && (! isprime(n)) && (! (ispower(n, , &p) && isprime(p))); \\ Michel Marcus, Jan 24 2014
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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