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A095739 Numbers known to be solitary but not coprime to sigma. +0
4
18, 45, 48, 52, 136, 148, 160, 162, 176, 192, 196, 208, 232, 244, 261, 272, 292, 296, 297, 304, 320, 352, 369 (list; graph; listen)
OFFSET

1,1

COMMENT

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.

"It is believed that 10, 14, 15, 20, 22, 26, 33, 34, 38, 44, 46, 51, 54, 58, 62, 68, 69, 70, 72, 74, 76, 82, 86, 87, 88, 90, 91, 92, 94, 95, 99, 104, 105, 106 and many others are also solitary, although a proof appears to be extremely difficult." Quote from Eric Weisstein. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Feb 02 2006

REFERENCES

Anderson, Claude W. and Hickerson, Dean; Advanced Problem 6020, "Friendly Integers", Amer. Math. Monthly, 1977, V84#1p65-6.

LINKS

Walter Nissen, Home Page (listed in lieu of email address)

Eric Weisstein's World of Mathematics, Solitary Number.

CROSSREFS

Cf. A095738, A074902.

Sequence in context: A045264 A049067 A114814 this_sequence A055577 A002798 A124388

Adjacent sequences: A095736 A095737 A095738 this_sequence A095740 A095741 A095742

KEYWORD

nonn

AUTHOR

Walter Nissen Jul 08 2004

EXTENSIONS

More terms from Frank Adams-Watters (FrankTAW(AT)Netscape.net), Feb 02 2006

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Last modified November 25 08:46 EST 2009. Contains 167481 sequences.


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