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!)
A320779 Inverse Euler transform of the number of divisors function A000005. 12
1, 1, 0, 0, -1, 1, -1, 0, 1, -1, 0, 1, -1, -1, 2, 1, -2, -2, 2, 3, -4, 0, 3, -3, 3, -2, -2, 2, 1, 7, -15, 0, 17, -11, -1, 0, 9, -4, -18, 26, -10, -10, 24, -17, -15, 21, 27, -42, -37, 69, 43, -113, -11, 149, -98, -24, 67, -57, 24, -53, 213, -243, -193, 704 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,15
COMMENTS
The Euler transform of a sequence q is the sequence of coefficients of x^n, n > 0, in the expansion of Product_{n > 0} 1/(1 - x^n)^q(n).
LINKS
OEIS Wiki, Euler transform
MAPLE
# The function EulerInvTransform is defined in A358451.
a := EulerInvTransform(n -> ifelse(n=0, 1, NumberTheory:-SumOfDivisors(n, 0))):
seq(a(n), n = 1..64); # Peter Luschny, Nov 21 2022
MATHEMATICA
EulerInvTransform[{}]={}; EulerInvTransform[seq_]:=Module[{final={}}, For[i=1, i<=Length[seq], i++, AppendTo[final, i*seq[[i]]-Sum[final[[d]]*seq[[i-d]], {d, i-1}]]];
Table[Sum[MoebiusMu[i/d]*final[[d]], {d, Divisors[i]}]/i, {i, Length[seq]}]];
EulerInvTransform[Table[DivisorSigma[0, n], {n, 100}]]
CROSSREFS
Cf. A000005.
Sequence in context: A323088 A052954 A123505 * A356876 A114920 A283190
KEYWORD
sign
AUTHOR
Gus Wiseman, Oct 22 2018
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 February 21 02:30 EST 2024. Contains 370219 sequences. (Running on oeis4.)