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 A336098 #17 Jul 19 2020 07:00:43 %S A336098 46,55,85,87,92,110,123,138,141,145,155,158,183,184,187,190,194,203, %T A336098 205,217,219,220,230,238,247,253,259,261,265,275,276,282,287,290,291, %U A336098 295,302,305,310,316,319,327,334,339,366,368,369,380,388,391,395,403,406,407,410,414,415,423,425,426,427,434 %N A336098 Numbers k such that equation x = k*sopf(x) has no solutions in positive integers. %C A336098 If k = p^s then p^(s+1) is solution of x = k*sopf(x). Hence powers of primes are not in the sequence. %C A336098 Let p_1*...*p_t is in the sequence. Then p_1^a_1*...*p_t^a_t is in the sequence for all positive integers a_1, ..., a_t. It means that the sequence is infinite. %H A336098 Vladimir Letsko, <a href="https://dxdy.ru/post1257616.html#p1257616">Mathematical Marathon, Problem 227</a> (in Russian). %o A336098 (PARI) sopf(n) = vecsum(factor(n)[, 1]); \\ A008472 %o A336098 pp(n) = prod(k=1, n, prime(k)); \\ A002110 %o A336098 sp(n) = sum(k=1, n, prime(k)); \\ A007504 %o A336098 ip(n) = {my(k=1); while (pp(k)/sp(k) <= n, k++); k+1;} %o A336098 listako(nn) = {my(lim = pp(ip(nn))); my(v = vector(lim, k, k++; k/sopf(k))); my(w = vector(nn-1, k, #select(x->(x==k+1), v))); apply(x->(x+1), Vec(select(x->(x==0), w, 1)));} \\ _Michel Marcus_, Jul 16 2020 %Y A336098 Cf. A008472, A336099. %K A336098 nonn %O A336098 1,1 %A A336098 _Vladimir Letsko_, Jul 08 2020