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A174961 Number of non-unitary divisors of the n-th nonsquarefree number. 5
1, 2, 1, 2, 3, 2, 2, 4, 1, 2, 2, 4, 5, 4, 2, 2, 6, 1, 2, 2, 4, 4, 4, 2, 5, 2, 8, 2, 2, 6, 3, 4, 4, 4, 2, 8, 2, 2, 5, 4, 8, 6, 2, 2, 8, 1, 2, 2, 4, 6, 4, 4, 4, 4, 11, 2, 2, 4, 4, 2, 4, 8, 6, 2, 8, 1, 2, 2, 2, 6, 10, 4, 2, 4, 10, 5, 4, 8, 4, 2, 6, 2, 12, 4, 8, 5, 4, 4, 4, 2, 12, 2, 4, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
The nonzero terms of A048105.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from G. C. Greubel)
FORMULA
From Amiram Eldar, Dec 09 2023: (Start)
a(n) = A048105(A013929(n)).
Sum_{k=1..n} a(k) ~ (n/zeta(2)) * (log(n) + 2*gamma - 1 - 2*zeta'(2)/zeta(2)), where gamma is Euler's constant (A001620). (End)
EXAMPLE
For n = 4, the fourth nonsquarefree number is A013929(4) = 12 which has 2 non-unitary divisors, 2 and 6. Therefore a(4) = 2.
MATHEMATICA
Select[Table[DivisorSigma[0, n] - 2^(PrimeNu[n]), {n, 1, 500}], # > 0 &] (* G. C. Greubel, May 21 2017 *)
PROG
(PARI) lista(kmax) = {my(f); for(k = 1, kmax, f = factor(k); if(!issquarefree(f), print1(numdiv(f) - 2^omega(f), ", "))); } \\ Amiram Eldar, Dec 09 2023
CROSSREFS
Sequence in context: A283845 A365543 A058071 * A104889 A356122 A290979
KEYWORD
nonn
AUTHOR
N. Wu (neil_wu0626(AT)yahoo.com), Apr 02 2010
EXTENSIONS
Edited by Amiram Eldar, Dec 09 2023
STATUS
approved

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Last modified March 28 08:12 EDT 2024. Contains 371236 sequences. (Running on oeis4.)