cp's OEIS Frontend

A122435 Complex numbers a+bi which are divisible by the sum of their complex prime factors with repetition (complex sopfr). The prime factors are from the first quadrant only, as defined in A103431. This sequence gives the real part a of these numbers, the imaginary part b is in A122436.

%I A122435 #10 Feb 03 2017 10:47:28
%S A122435 10,15,16,27,30,17,34,39,14,38,14,44,48,39,40,1,57,45,54,28,64,21,46,
%T A122435 57,72,45,75,44,64,38,70,4,84,72,60,70,78,100,53,89,52,90,5,105,6,42,
%U A122435 104,70,90,114
%N A122435 Complex numbers a+bi which are divisible by the sum of their complex prime factors with repetition (complex sopfr). The prime factors are from the first quadrant only, as defined in A103431. This sequence gives the real part a of these numbers, the imaginary part b is in A122436.
%C A122435 In the case of the complex sopfr it seems best to use only primes in the first quadrant because it is easy to get a well-defined function.
%H A122435 Sven Simon, <a href="/A122435/a122435.txt">Readable list of A122435/A122436</a>
%H A122435 R. Spira, <a href="http://www.jstor.org/stable/2312472">The Complex Sum Of Divisors</a>, American Mathematical Monthly, 1961 Vol. 68, pp. 120-124.
%e A122435 a(1) = 10 is the real part of 10 = (-1)*(1+i)*(1+i)*(1+2i)*(2+i) = (1-i)(5+5i); (1+i)+(1+i)+(1+2i)+(2+i) = 5+5i;
%e A122435 a(5) = 30 is the real part of 30+12i = (-i)*3*(1+i)*(1+i)*(5+2i) = 3*(10+4i); 3+(1+i)+(1+i)+(5+2i) = 10+4i.
%Y A122435 Cf. A103431, A103432.
%K A122435 nonn
%O A122435 1,1
%A A122435 _Sven Simon_, Sep 04 2006