A095739 Numbers known to be solitary but not coprime to sigma.

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

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