The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A085410 Total number of parts in all partitions of n into relatively prime parts. 4
 1, 2, 5, 9, 19, 27, 53, 74, 122, 170, 274, 355, 555, 724, 1043, 1377, 1964, 2487, 3497, 4429, 5993, 7622, 10205, 12701, 16831, 20964, 27166, 33756, 43452, 53296, 68134, 83464, 105086, 128495, 160803, 195006, 242811, 293701, 362026, 436842, 536103 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Table of n, a(n) for n=1..41. FORMULA Moebius transform of A006128: Sum_{d|n} mu(n/d)*A006128(d). EXAMPLE Partitions of 6 into relatively prime parts are: 1+1+1+1+1+1, 1+1+1+1+2, 1+1+2+2, 1+1+1+3, 1+2+3, 1+1+4, 1+5; total number of parts is a(6)=6+5+4+4+3+3+2=27. MATHEMATICA f[n_] := Sum[DivisorSigma[0, m] PartitionsP[n - m], {m, 1, n}]; MT[n_] := Block[{d = Divisors[n]}, Plus @@ (MoebiusMu /@ (n/d)*f /@ d)]; Table[ MT[n], {n, 1, 41}] PROG (PARI) a006128(n) = sum(m=1, n, numdiv(m)*numbpart(n - m)); a(n) = sumdiv(n, d, moebius(n/d)*a006128(d)); \\ Indranil Ghosh, Apr 25 2017 (Python) from sympy import divisors, divisor_count, npartitions, mobius def a006128(n): return sum([divisor_count(m)*npartitions(n - m) for m in range(1, n + 1)]) def a(n): return sum([mobius(n/d)*a006128(d) for d in divisors(n)]) # Indranil Ghosh, Apr 25 2017 CROSSREFS Cf. A000837. Sequence in context: A342013 A213544 A265482 * A073118 A048082 A089089 Adjacent sequences: A085407 A085408 A085409 * A085411 A085412 A085413 KEYWORD easy,nonn AUTHOR Vladeta Jovovic, Aug 13 2003 EXTENSIONS More terms from Robert G. Wilson v, Aug 17 2003 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.

Last modified May 23 16:36 EDT 2024. Contains 372765 sequences. (Running on oeis4.)