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A095738
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Numbers that are solitary because they are coprime to sigma but are not prime powers.
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3
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| 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 iff they have the same abundancy. E.g. abund ( 12 ) = abund ( 234 ) = 7 / 3 ===> 12 and 234 are friends.
Integers which have no friends are called solitary.
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REFERENCES
| Anderson, Claude W. and Hickerson, Dean; Advanced Problem 6020, "Friendly Integers", Amer. Math. Monthly, 1977, V84#1p65-6.
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LINKS
| Walter Nissen, Home Page (listed in lieu of email address)
Walter Nissen, Primitive Friendly Integers and Exclusive Multiples, 2004 post to NMBRTHRY mailing list
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CROSSREFS
| Cf. A014567, A074902, A095739.
Sequence in context: A053409 A144205 A008946 * A138227 A155710 A001491
Adjacent sequences: A095735 A095736 A095737 * A095739 A095740 A095741
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KEYWORD
| nonn
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AUTHOR
| Walter Nissen Jul 08 2004
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