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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

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: A286713 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

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Last modified April 3 00:35 EDT 2020. Contains 333195 sequences. (Running on oeis4.)