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.
Select[Range[2, 1300000], Mod[Sum[DivisorSigma[1, k] - k, {k, 1, #}], Sum[DivisorSigma[0, k] - 1, {k, 1, #}]] == 0 &]
3 is a term because the first 3 terms of A007947 are 1, 2 and 3 whose sum is divisible by 3.
isok(k) = sum(i=1, k, factorback(factor(i)[, 1])) % k == 0; \\ Michel Marcus, Apr 25 2018
5 is in the sequence because the distinct prime factors of 2, 3, 4, and 5 are 2, 3, 2 and 5 respectively and their average (2 + 3 + 2 + 5) / 4 = 3 is an integer. - _David A. Corneth_, Apr 26 2018
s = t = 0; k = 2; lst = {}; While[k < 1000000000, p = #[[1]] & /@ FactorInteger@ k; s = s + Plus @@ p; t = t + Length@ p; If[ Mod[s, t] == 0, AppendTo[lst, k]]; k++]; lst (* Robert G. Wilson v, Apr 26 2018 *)
6 is in the sequence because (gpf(2) + gpf(3) + gpf(4) + gpf(5) + gpf(6))/5 = (2 + 3 + 2 + 5 + 3)/5 = 3 is an integer.
isok(n) = (n>1) && !(sum(k=2, n, vecmax(factor(k)[,1])) % (n-1)); \\ Michel Marcus, Apr 29 2018
lista(nn) = {s = 0; for (n=2, nn, s += vecmax(factor(n)[,1]); if (! (s % (n-1)), print1(n, ", ")););} \\ Michel Marcus, Apr 29 2018
phi(1) + phi(2) + phi(3) + phi(4) + phi(5) = 1 + 1 + 2 + 2 + 4 = 10; d(1) + d(2) + d(3) + d(4) + d(5) = 1 + 2 + 2 + 3 + 2 = 10; Finally 10 / 10 = 1.
[n:n in [1..1000]| IsIntegral(&+[EulerPhi(m):m in [1..n]]/&+[NumberOfDivisors(m):m in [1..n]])] ; // Marius A. Burtea, Mar 25 2019
with(numtheory):P:=proc(q) local a,b,n; a:=0; b:=0; for n from 1 to q do a:=a+tau(n); b:=b+phi(n); if type(b/a,integer) then print(n); fi; od; end: P(10^10);
lista(nn) = {se = 0; sn = 0; for (n=1, nn, se += eulerphi(n); sn += numdiv(n); if (se % sn == 0, print1(n, ", ")););} \\ Michel Marcus, Nov 01 2014
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