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A122435
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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.
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2
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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
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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