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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
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
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Aug 13 2003
EXTENSIONS
More terms from Robert G. Wilson v, Aug 17 2003
STATUS
approved

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