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A140238
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Numbers k such that Sum_{i=1..k} d(i) is coprime to d(k), where d(k) is the number of positive divisors of k.
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2
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1, 2, 3, 4, 9, 10, 11, 12, 13, 14, 15, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 62, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 93, 94, 95, 97, 98, 99, 100, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135
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OFFSET
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1,2
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COMMENTS
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Sum_{k=1..n} d(k) = Sum_{k=1..n} floor(n/k) = A006218(n).
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LINKS
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MAPLE
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N:= 1000: # for terms <= N
T:= map(numtheory:-tau, [$1..N]):
S:= ListTools:-PartialSums(T):
select(t -> igcd(T[t], S[t])=1, [$1..N]); # Robert Israel, Oct 24 2023
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PROG
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(Python)
from math import gcd, isqrt
from sympy import divisor_count
def A140238_gen(startvalue=1): # generator of terms >= startvalue
return filter(lambda n: gcd(divisor_count(n), -(s:=isqrt(n))**2+(sum(n//k for k in range(1, s+1))<<1))==1, count(max(startvalue, 1)))
(PARI) isok(k) = gcd(sum(i=1, k, k\i), numdiv(k)) == 1; \\ Michel Marcus, Oct 29 2023
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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