OFFSET
1,1
COMMENTS
If k = p^s then p^(s+1) is solution of x = k*sopf(x). Hence powers of primes are not in the sequence.
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.
LINKS
Vladimir Letsko, Mathematical Marathon, Problem 227 (in Russian).
PROG
(PARI) sopf(n) = vecsum(factor(n)[, 1]); \\ A008472
pp(n) = prod(k=1, n, prime(k)); \\ A002110
sp(n) = sum(k=1, n, prime(k)); \\ A007504
ip(n) = {my(k=1); while (pp(k)/sp(k) <= n, k++); k+1; }
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
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Letsko, Jul 08 2020
STATUS
approved