This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A301975 #21 Nov 06 2019 03:46:34 %S A301975 1,3,5,6,7,11,13,14,17,19,22,23,28,29,31,37,38,41,43,45,46,47,52,53, %T A301975 56,59,60,61,62,67,71,73,76,79,83,86,89,94,96,97,99,101,103,107,109, %U A301975 113,118,124,126,127,130,131,132,134,137,139,142,147,148,149,150,151,153,157,158,163,166,167,168,170,172,173,175,176,179 %N A301975 Numbers whose abundance is divisible by its number of divisors. %C A301975 Numbers n such that f(n) = A033880(n)/A000005(n) is an integer. %C A301975 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. %C A301975 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. %H A301975 Giovanni Resta, <a href="/A301975/b301975.txt">Table of n, a(n) for n = 1..10000</a> %e A301975 11 is a term as its abundance is -10 and its number of divisors is 2, the former number being divisible by the latter. %t A301975 Select[Range[180], Divisible[DivisorSigma[1,#]-2#, DivisorSigma[0,#]]&] %o A301975 (PARI) for(n=1, 180, ((sigma(n)-2*n)%numdiv(n)==0) && print1(n ", ")) %o A301975 (PARI) isok(n) = !((sigma(n)-2*n)%numdiv(n)); \\ _Michel Marcus_, Apr 09 2018 %Y A301975 Cf. A033880 (abundance), A000005 (number of divisors), A065091, A000396 (subsequences), A056075 (related sequence). %K A301975 nonn %O A301975 1,2 %A A301975 _Waldemar Puszkarz_, Mar 29 2018