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A152770
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Sum of proper divisors minus the number of proper divisors of n: a(n) = sigma(n) - n - d(n) + 1.
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22
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0, 0, 0, 1, 0, 3, 0, 4, 2, 5, 0, 11, 0, 7, 6, 11, 0, 16, 0, 17, 8, 11, 0, 29, 4, 13, 10, 23, 0, 35, 0, 26, 12, 17, 10, 47, 0, 19, 14, 43, 0, 47, 0, 35, 28, 23, 0, 67, 6, 38, 18, 41, 0, 59, 14, 57, 20, 29, 0, 97, 0, 31, 36, 57, 16, 71, 0, 53, 24, 67, 0, 112, 0, 37, 44, 59, 16, 83, 0, 97
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,6
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COMMENTS
| Sum of divisors of n, minus the number of divisors of n, minus n, plus 1.
Also, sum of proper divisors of n, minus the number of divisors of n, plus 1.
Note that if a(n)>0 then n is a composite number (A002808), otherwise, n is a non-composite number (A008578) also called prime number at the beginning of the 20th century.
Also, sum of divisors of n, minus the number of proper divisors of n, minus n. [From Omar E. Pol (info(AT)polprimos.com), Dec 14 2008]
a(A008578)==0. [From Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 14 2008]
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FORMULA
| a(n) = A000203(n)-A000005(n)-n+1 = A001065(n)-A000005(n)+1 = A000203(n)-A062249(n)+1 = A065608(n)-n+1.
a(n) = A000203(n)-A032741(n)-n. [From Omar E. Pol (info(AT)polprimos.com), Dec 14 2008]
a(n) = A001065(n)-A032741(n). [From Omar E. Pol (info(AT)polprimos.com), Dec 15 2008]
a(n)= A158901(n)-n. [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Sep 12 2009]
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MAPLE
| A152770 := proc(n)
numtheory[sigma](n)-n-numtheory[tau](n)+1 ;
end proc: # R. J. Mathar, Sep 28 2011
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MATHEMATICA
| f[n_] := DivisorSigma[1, n] - DivisorSigma[0, n] - n + 1; Array[f, 105] [From Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 14 2008]
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CROSSREFS
| A000005, A000040, A000203, A001065, A002808, A008578, A062249, A065608.
Cf. A032741. [From Omar E. Pol (info(AT)polprimos.com), Dec 14 2008]
Sequence in context: A201291 A077150 A065453 * A098601 A113486 A108572
Adjacent sequences: A152767 A152768 A152769 * A152771 A152772 A152773
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KEYWORD
| easy,nonn
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AUTHOR
| Omar E. Pol (info(AT)polprimos.com), Dec 12 2008
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EXTENSIONS
| More term from Omar E. Pol (info(AT)polprimos.com) and Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 14 2008
Definition clarified and edited by Omar E. Pol (info(AT)polprimos.com), Dec 21 2008
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