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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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
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.
"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. Adams-Watters, Feb 02 2006
LINKS
Claude W. Anderson and Dean Hickerson, Advanced Problem 6020: Friendly Integers, Amer. Math. Monthly, 1977, V84#1p65-6.
Eric Weisstein's World of Mathematics, Solitary Number.
CROSSREFS
Sequence in context: A114814 A299383 A177724 * A055577 A281917 A002798
KEYWORD
nonn
AUTHOR
Walter Nissen, Jul 08 2004
EXTENSIONS
More terms from Franklin T. Adams-Watters, Feb 02 2006
STATUS
approved

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Last modified March 19 06:56 EDT 2024. Contains 370953 sequences. (Running on oeis4.)