login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A283763 Number of ways of writing n as sum of a deficient number (A005100) and abundant number (A005101). 1
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 2, 2, 3, 3, 3, 1, 4, 3, 4, 4, 4, 1, 5, 3, 5, 5, 5, 1, 6, 4, 6, 4, 7, 2, 8, 6, 8, 6, 8, 1, 9, 7, 9, 6, 9, 2, 10, 8, 11, 8, 11, 1, 12, 9, 12, 9, 12, 3, 13, 8, 13, 10, 14, 4, 15, 11, 15, 9, 15, 4, 16, 11, 17, 12, 17, 4, 18, 13, 18, 13, 19, 4, 20, 14, 20, 14, 20 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,20
LINKS
Eric Weisstein's World of Mathematics, Abundant Number
Eric Weisstein's World of Mathematics, Deficient Number
FORMULA
G.f.: (Sum_{i>=1} x^A005100(i))*(Sum_{j>=1} x^A005101(j)).
EXAMPLE
a(21) = 3 because we have [20, 1], [18, 3] and [12, 7].
MATHEMATICA
nmax = 95; CoefficientList[Series[Sum[Boole[DivisorSigma[1, k] > 2 k] x^k, {k, 1, nmax}] Sum[Boole[DivisorSigma[1, k] < 2 k] x^k, {k, 1, nmax}], {x, 0, nmax}], x]
PROG
(PARI) concat([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], Vec(sum(k=1, 95, (sigma(k)>2*k) * x^k) * sum(k=1, 95, (sigma(k)<2*k) * x^k) + O(x^96))) \\ Indranil Ghosh, Mar 16 2017
CROSSREFS
Sequence in context: A131619 A048485 A127714 * A357622 A357621 A220604
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Mar 16 2017
STATUS
approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 16:34 EDT 2024. Contains 371254 sequences. (Running on oeis4.)