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

 Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A157449 Difference between n and the sum of its divisors except 1 and itself. 2
 2, 3, 2, 5, 1, 7, 2, 6, 3, 11, -3, 13, 5, 7, 2, 17, -2, 19, -1, 11, 9, 23, -11, 20, 11, 15, 1, 29, -11, 31, 2, 19, 15, 23, -18, 37, 17, 23, -9, 41, -11, 43, 5, 13, 21, 47, -27, 42, 8, 31, 7, 53, -11, 39, -7, 35, 27, 59, -47, 61, 29, 23, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS a(n) = n - k where k is the sum of the divisors of n excluding 1 and n itself. The initial value for n is 2. Evidently a(n) = n iff n is prime (A000040). Moreover a(n) = 1 iff n is perfect (A000396). A value of 0 indicates a quasiperfect number, although no such number is known. - Felix Fröhlich, Jul 14 2014 LINKS F. Guidi, Table of n, a(n) for n=2,...,100001 Wikipedia, Quasiperfect number - Felix Fröhlich, Jul 14 2014 FORMULA a(n) = (2*n+1)-A000203(n). - Felix Fröhlich, Jul 14 2014 EXAMPLE The divisors of 10 are 1, 2, 5 and 10, so a(10) = 10 - (2 + 5) = 3. MATHEMATICA Table[2n+1-DivisorSigma[1, n], {n, 70}] (* Harvey P. Dale, Jul 22 2013 *) PROG (PARI) for(n=2, 1e2, a=2*n+1; b=sigma(n); print1(a-b, ", ")) \\ Felix Fröhlich, Jul 14 2014 CROSSREFS Cf. A000040, A000396. Sequence in context: A332881 A332424 A293212 * A053139 A127705 A124386 Adjacent sequences:  A157446 A157447 A157448 * A157450 A157451 A157452 KEYWORD sign AUTHOR Ferruccio Guidi (fguidi(AT)cs.unibo.it), Mar 01 2009 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 November 30 05:31 EST 2020. Contains 338781 sequences. (Running on oeis4.)