The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A240923 a(n) = numerator(sigma(n)/n) - sigma(denominator(sigma(n)/n)). 4
 0, 0, 0, 0, 0, 1, 0, 0, 0, 3, 0, 3, 0, 4, 2, 0, 0, 1, 0, 3, 0, 6, 0, 2, 0, 7, 0, 1, 0, 6, 0, 0, 4, 9, 0, 0, 0, 10, 0, 2, 0, 8, 0, 9, 2, 12, 0, 3, 0, 0, 6, 7, 0, 7, 0, 7, 0, 15, 0, 8, 0, 16, 0, 0, 0, 12, 0, 9, 8, 24, 0, 5, 0, 19, 0, 15, 0, 14, 0, 3, 0, 21, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,10 COMMENTS a(n) is the integer t, such that if sigma(n)/n is written in its most reduced form, nk/dk = A017665(n)/A017666(n), then we have (sigma(dk)+t)/dk. It appears that a(n) is never negative. a(n) = 0 if and only if n is in A014567 (n and sigma(n) are relatively prime). LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 William G. Stanton and Judy A. Holdener, Abundancy "Outlaws" of the Form (sigma(N) + t)/N, Journal of Integer Sequences , Vol 10 (2007) , Article 07.9.6. EXAMPLE For n=10, sigma(10)/10 = 18/10 = 9/5 = (sigma(5) + 3)/5, hence a(10)=3. MAPLE with(numtheory): A240923:=n->numer(sigma(n)/n) - sigma(denom(sigma(n)/n)): seq(A240923(n), n=1..100); # Wesley Ivan Hurt, Aug 06 2014 MATHEMATICA Table[Numerator[DivisorSigma[1, n]/n] - DivisorSigma[1, Denominator[ DivisorSigma[1, n]/n]], {n, 100}] (* Wesley Ivan Hurt, Aug 06 2014 *) PROG (PARI) a(n) = my(ab = sigma(n)/n); numerator(ab) - sigma(denominator(ab)); (Haskell) import Data.Ratio ((%), numerator, denominator) a240923 n = numerator sq - a000203 (denominator sq)    where sq = a000203 n % n -- Reinhard Zumkeller, Aug 05 2014 (Python) from gmpy2 import mpq from sympy import divisors map(lambda x: x.numerator-sum(divisors(x.denominator)), [mpq(sum(divisors(n)), n) for n in range(1, 10**5)]) # Chai Wah Wu, Aug 05 2014 CROSSREFS Cf. A014567, A017665, A017666. Cf. A000203. Sequence in context: A297871 A292130 A291971 * A272727 A333791 A323135 Adjacent sequences:  A240920 A240921 A240922 * A240924 A240925 A240926 KEYWORD nonn AUTHOR Michel Marcus, Aug 03 2014 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 20 23:46 EDT 2021. Contains 343143 sequences. (Running on oeis4.)