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A360940
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Numbers k such that k / A000005(k) + k / A000010(k) is an integer.
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0
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1, 2, 3, 8, 10, 12, 18, 21, 24, 28, 36, 72, 78, 96, 108, 126, 128, 168, 224, 243, 288, 294, 384, 392, 756, 864, 930, 972, 1000, 1152, 1323, 1350, 1944, 2310, 2430, 2530, 2808, 3087, 3456, 4116, 6144, 6912, 7776, 10206, 10584, 13122, 13230, 13500, 13608, 18432
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OFFSET
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1,2
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COMMENTS
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It seems that odd k's {1, 3, 21, 243, 1323, 3087, ...} are relatively rare. A235353 is a subsequence of this sequence.
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LINKS
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EXAMPLE
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and so on.
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MATHEMATICA
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Select[Range[10^4], IntegerQ[#/DivisorSigma[0, #] + #/EulerPhi[#]] &] (* Amiram Eldar, Feb 26 2023 *)
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PROG
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(Python)
from math import prod
from itertools import count, islice
from sympy import factorint
def A360940_gen(startvalue=1): # generator of terms >= startvalue
for k in count(max(startvalue, 1)):
f = factorint(k)
t = prod(p**(e-1)*(p-1) for p, e in f.items())
s = prod(e+1 for e in f.values())
if not k*(s+t)%(s*t):
yield k
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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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