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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 Table of n, a(n) for n=1..23. 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 Cf. A095738, A074902. Sequence in context: A114814 A299383 A177724 * A055577 A281917 A002798 Adjacent sequences: A095736 A095737 A095738 * A095740 A095741 A095742 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 November 30 18:31 EST 2023. Contains 367461 sequences. (Running on oeis4.)