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.

10, 15, 16, 27, 30, 17, 34, 39, 14, 38, 14, 44, 48, 39, 40, 1, 57, 45, 54, 28, 64, 21, 46, 57, 72, 45, 75, 44, 64, 38, 70, 4, 84, 72, 60, 70, 78, 100, 53, 89, 52, 90, 5, 105, 6, 42, 104, 70, 90, 114

Offset

1,1

Comments

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.

Links

Table of n, a(n) for n=1..50.

Sven Simon, Readable list of A122435/A122436

R. Spira, The Complex Sum Of Divisors, American Mathematical Monthly, 1961 Vol. 68, pp. 120-124.

Example

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;
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.

Crossrefs

Cf. A103431, A103432.

Sequence in context: A342593 A046424 A076226 * A091049 A188579 A269985

Adjacent sequences: A122432 A122433 A122434 * A122436 A122437 A122438

Keyword

nonn

Author

Sven Simon, Sep 04 2006

Status

approved