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A095751
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Integers known to be friendly but are not known to be primitive friendly.
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1
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66, 78, 102, 114, 120, 132, 138, 150, 174, 186, 204, 222, 228, 246, 252, 258, 276, 280, 282, 294, 300, 308, 312, 318, 330, 348, 354, 360, 364, 366, 372
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OFFSET
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1,1
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COMMENTS
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There may be other integers in the sequence within the range of those given, but they have yet to be calculated and moreover, some of these given may prove to be primitive friendly.
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.
Friends m and n are primitive friendly iff they have no common prime factor of the same multiplicity.
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REFERENCES
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Anderson, Claude W. and Hickerson, Dean; Advanced Problem 6020, "Friendly Integers", Amer. Math. Monthly, 1977, V84#1p65-6.
Hickerson, Dean; "Re: Friendly number", post to sci.math newsgroup, 2000, available through groups.google.com.
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LINKS
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Table of n, a(n) for n=1..31.
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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EXAMPLE
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66 is a friend of 308, 5456, 89408 and 369053696, but all of these are divisible by 11 and not 121, while 66 is not known to be primitive friendly.
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CROSSREFS
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Cf. A014567, A074902, A095738, A095739, A096366.
Sequence in context: A124142 A036207 A039538 * A121478 A128896 A109750
Adjacent sequences: A095748 A095749 A095750 * A095752 A095753 A095754
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KEYWORD
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nonn
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AUTHOR
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Walter Nissen Jul 09 2004
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STATUS
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approved
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