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 A307888 #58 May 14 2019 11:02:00 %S A307888 6,234,588,600,6552,89376,209195610624 %N A307888 Non-coreful perfect numbers. %C A307888 A coreful divisor d of a number k is a divisor with the same set of distinct prime factors as k (see LINKS). %C A307888 Here, only the non-coreful divisors of k are considered. %H A307888 G. E. Hardy and M. V. Subbarao, <a href="/A005934/a005934.pdf">Highly powerful numbers</a>, Congress. Numer. 37 (1983), 277-307. (Annotated scanned copy) %F A307888 Solutions of k = A000203(k) - A057723(k). %e A307888 Divisors of 234 are 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234 and its prime factors are 2, 3, 13. Among the divisors, 78 and 234 are divided by all the prime factors and 1 + 2 + 3 + 6 + 9 + 13 + 18 + 26 + 39 + 117 = 234. %p A307888 with(numtheory): P:=proc(q) local a,k,n; for n from 1 to q do %p A307888 a:=mul(k,k=factorset(n)); if n=sigma(n)-a*sigma(n/a) then print(n); fi; %p A307888 od; end: P(10^7); %t A307888 f[p_, e_] := (p^(e + 1) - 1)/(p - 1); fc[p_, e_] := f[p, e] - 1; ncQ[n_] := Times @@ (f @@@ FactorInteger[n]) - Times @@ (fc @@@ FactorInteger[n]) == n; Select[Range[2, 10^5], ncQ] (* _Amiram Eldar_, May 11 2019 *) %o A307888 (PARI) rad(n) = factorback(factorint(n)[, 1]); \\ A007947 %o A307888 s(n) = rad(n)*sigma(n/rad(n)); \\ A057723 %o A307888 isok(n) = sigma(n) - s(n) == n; \\ _Michel Marcus_, May 11 2019 %Y A307888 Cf. A000203, A007947, A057723, A307958, A307986, A308029. %K A307888 nonn,more %O A307888 1,1 %A A307888 _Paolo P. Lava_, May 09 2019 %E A307888 a(7) from _Giovanni Resta_, May 09 2019