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A324710 Number x such that x = Sum_{i=1..k}{sigma(x/p_i)}, where p_i are the k prime factors of x. 2

%I

%S 1748,5588,138128,1683728,9286208,12642368,152287808,447483968

%N Number x such that x = Sum_{i=1..k}{sigma(x/p_i)}, where p_i are the k prime factors of x.

%C All the terms appear to be multiples of 4.

%C a(9) > 2*10^11. Up to a(8) all the terms are of the form 2^k * p * q, with p and q primes. The next such terms in the sequence are 2^16*197539*41626667, 2^16*196817*183392089, and 2^20*3360697*49177969. - _Giovanni Resta_, Mar 14 2019

%e Prime factors of 1748 are 2, 19, 23 and sigma(1748/2) + sigma(1748/19) + sigma(1748/23) = 1440 + 168 + 140 = 1748.

%p with(numtheory): P:=proc(q) local k,n; for n from 1 to q do

%p if n=add(sigma(n/k),k=factorset(n)) then print(n);

%p fi; od; end: P(10^9);

%o (PARI) isok(x) = my(f=factor(x)[,1]~); x == sum(k=1, #f, sigma(x/f[k])); \\ _Michel Marcus_, Mar 15 2019

%Y Cf. A000203, A324711.

%K nonn,hard,more

%O 1,1

%A _Paolo P. Lava_, Mar 13 2019

%E a(7)-a(8) from _Giovanni Resta_, Mar 14 2019

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Last modified September 16 15:58 EDT 2021. Contains 347473 sequences. (Running on oeis4.)