

A095739


Numbers known to be solitary but not coprime to sigma.


3



18, 45, 48, 52, 136, 148, 160, 162, 176, 192, 196, 208, 232, 244, 261, 272, 292, 296, 297, 304, 320, 352, 369
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OFFSET

1,1


COMMENTS

Abundancy is defined as the ratio of the multiplicative sumofdivisors 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 W. Weisstein.  Franklin T. AdamsWatters, Feb 02 2006


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KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



