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A362864
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Numbers k that divide Sum_{i=1..k} (i - d(i)), where d(n) is the number of divisors of n (A000005).
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1
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1, 2, 5, 8, 15, 24, 26, 47, 121, 204, 347, 562, 4204, 6937, 6947, 31108, 379097, 379131, 379133, 2801205, 12554202, 20698345, 56264197, 13767391064, 37423648626, 37423648726, 61701166395, 276525443156, 276525443176, 455913379395, 455913379831, 751674084802
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OFFSET
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1,2
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COMMENTS
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Numbers k such that the mean number of nondivisors in the range 1..k is an integer.
Numbers k such that A161664(k) is divisible by k.
The subsequence of odd terms k equals the intersection of A050226 and this sequence.
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LINKS
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EXAMPLE
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k = 5: Sum_{i=1..5} (i - d(i))/k = 5/5 = 1, so k = 5 is a term.
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MATHEMATICA
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seq[kmax_] := Module[{sum = 0, s = {}}, Do[sum += k - DivisorSigma[0, k]; If[Divisible[sum, k], AppendTo[s, k]], {k, 1, kmax}]; s]; seq[10^6] (* Amiram Eldar, May 06 2023 *)
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PROG
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(PARI) isok(k) = !(sum(i=1, k, i - numdiv(i)) % k); \\ Michel Marcus, May 06 2023
(Python)
from itertools import count, islice
from sympy import divisor_count
def A362864_gen(): # generator of terms
c = 0
for k in count(1):
if not (c:=c+k-divisor_count(k))%k:
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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EXTENSIONS
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STATUS
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approved
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