OFFSET
1,2
COMMENTS
Perfect numbers (A000396) and odd primes (A065091) are members, unified (along with 1) into a subsequence on which abs(f(n)) reaches record extrema. For perfect numbers, these are global minima, for the other terms, maxima.
Another notable subsequence is defined by f(n)=1: numbers whose abundance equals their number of divisors. They all belong to A056075. The first 3 terms are 56, 7192, 7232. There are 11 of them up to 10^9.
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..10000
EXAMPLE
11 is a term as its abundance is -10 and its number of divisors is 2, the former number being divisible by the latter.
MATHEMATICA
Select[Range[180], Divisible[DivisorSigma[1, #]-2#, DivisorSigma[0, #]]&]
PROG
(PARI) for(n=1, 180, ((sigma(n)-2*n)%numdiv(n)==0) && print1(n ", "))
(PARI) isok(n) = !((sigma(n)-2*n)%numdiv(n)); \\ Michel Marcus, Apr 09 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Waldemar Puszkarz, Mar 29 2018
STATUS
approved