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A262870 Sum of the squarefree numbers appearing among the larger parts of the partitions of n into two parts. 7
0, 1, 2, 5, 3, 8, 11, 18, 18, 18, 23, 34, 28, 41, 48, 63, 63, 80, 80, 99, 89, 110, 121, 144, 144, 144, 157, 157, 143, 172, 187, 218, 218, 251, 268, 303, 303, 340, 359, 398, 398, 439, 460, 503, 481, 481, 504, 551, 551, 551, 551, 602, 576, 629, 629, 684, 684 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..57.

Index entries for sequences related to partitions

FORMULA

a(n) = Sum_{i=1..floor(n/2)} (n-i) * mu(n-i)^2, where mu is the Möebius function (A008683).

a(n) = A262992(n) - A262871(n).

EXAMPLE

a(4)=5; there are two partitions of 4 into two parts: (3,1) and (2,2). The sum of the larger squarefree parts is 3+2=5, thus a(4)=5.

a(5)=3; there are two partitions of 5 into two parts: (4,1) and (3,2). Of the larger parts, 3 is the only squarefree part, so a(5)=3.

MAPLE

with(numtheory): A262870:=n->add((n-i)*mobius(n-i)^2, i=1..floor(n/2)): seq(A262870(n), n=1..100);

MATHEMATICA

Table[Sum[(n - i) MoebiusMu[n - i]^2, {i, Floor[n/2]}], {n, 70}]

PROG

(PARI) a(n) = sum(i=1, n\2, (n-i) * moebius(n-i)^2); \\ Michel Marcus, Oct 04 2015

(PARI) a(n)=my(s); forsquarefree(k=(n+1)\2, n-1, s += k[1]); s \\ Charles R Greathouse IV, Jan 08 2018

CROSSREFS

Cf. A008683, A071068, A261985, A262351, A262868, A262869, A262871, A262991, A262992.

Sequence in context: A302054 A081146 A261927 * A294210 A244418 A082652

Adjacent sequences:  A262867 A262868 A262869 * A262871 A262872 A262873

KEYWORD

nonn,easy

AUTHOR

Wesley Ivan Hurt, Oct 03 2015

STATUS

approved

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Last modified July 29 14:59 EDT 2021. Contains 346346 sequences. (Running on oeis4.)