A100696 Weird numbers m such that the sum of their divisors below A033880(m) is greater than A033880(m) = abundance of m.

9272, 222952, 243892, 338572, 343876, 351956, 407132, 410476, 465652, 1188256, 1229152, 1901728, 2081824, 2189024, 3963968, 4199030, 4486208, 4559552, 5440192, 5568448, 5681270, 5763310, 5780810, 5804330, 5823790, 5921090, 6365870, 6460864, 6543110, 6911512

Offset: 1

Author

N. J. A. Sloane, based on email from Alexey Aleksandrov (aleksandrov1988(AT)gmail.com), Mar 28 2006

Keywords

• nonn

Comments

This sequence was posed as a puzzle by Prof. E. A. Roganov from Moscow State Industrial University at one of his seminars. It remained unsolved for several years. The solution (cf. current definition) was eventually revealed by the author (communicated by Max Alekseyev on Apr 19 2012).

It may be easily noticed that for an abundant number m, if the sum of its divisors below A033880(m) is smaller than A033880(m), then m is necessarily weird. So A100696 lists those weird numbers that cannot be detected this way. - Max Alekseyev, Apr 19 2012

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Donovan Johnson)

Crossrefs

Cf. A033880.

Intersection of A006037 and A182225.

Programs

PARI

is_A100696(n,d=divisors(n)[^-1],a=vecsum(d)-n,s=a)={for(i=1,#d,d[i]0||break); !is_A005835(n,d,a+n)} \\ M. F. Hasler, Jul 30 2016

Extensions

a(14)-a(30) from Donovan Johnson, Apr 19 2012

Data up to 10^7 double-checked by M. F. Hasler, Jul 30 2016