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A036347
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Numbers k for which the parity of k and the parity of sopfr(k) differ, where sopfr is the sum of prime factors with repetition.
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4
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1, 6, 9, 10, 12, 14, 15, 20, 21, 22, 24, 25, 26, 28, 33, 34, 35, 38, 39, 40, 44, 46, 48, 49, 51, 52, 54, 55, 56, 57, 58, 62, 65, 68, 69, 74, 76, 77, 80, 81, 82, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 104, 106, 108, 111, 112, 115, 116, 118, 119, 121, 122, 123, 124, 126, 129, 133, 134, 135, 136
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OFFSET
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1,2
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COMMENTS
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Parity of n and its sum of prime factors differs (counted with multiplicity). - The original name.
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LINKS
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FORMULA
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EXAMPLE
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111 = 3 * 37 -> sum = 40 so 111 is odd while 40 is even.
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PROG
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(Python)
from itertools import count, islice
from functools import reduce
from operator import ixor
from sympy import factorint
def A036347_gen(startvalue=1): # generator of terms
return filter(lambda n:(reduce(ixor, (p*e for p, e in factorint(n).items()), 0)^n)&1, count(max(startvalue, 1)))
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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Missing initial term a(1) = 1 prepended, offset corrected, name edited and more terms added by Antti Karttunen, Jan 15 2023
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STATUS
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approved
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