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A234306 a(n) = n + 1 - d(2n), where d(n) is the number of divisors of n. 2
0, 0, 0, 1, 2, 1, 4, 4, 4, 5, 8, 5, 10, 9, 8, 11, 14, 10, 16, 13, 14, 17, 20, 15, 20, 21, 20, 21, 26, 19, 28, 26, 26, 29, 28, 25, 34, 33, 32, 31, 38, 31, 40, 37, 34, 41, 44, 37, 44, 42, 44, 45, 50, 43, 48, 47, 50, 53, 56, 45, 58, 57, 52, 57, 58, 55, 64, 61 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Number of partitions of 2n into exactly two parts: (2n-i,i) such that i does not divide 2n-i. Complement of A066660.

LINKS

Muniru A Asiru, Table of n, a(n) for n = 1..5000

Index entries for sequences related to partitions

FORMULA

a(n) = n + 1 - A000005(2n).

a(n) = n - A066660(n).

a(n) = Sum_{i=1..n | i does not divide 2n-i} 1.

EXAMPLE

a(6) = 1; In this case, 2(6) = 12 has exactly 6 partitions into two parts: (11,1), (10,2), (9,3), (8,4), (7,5), (6,6).  Note that 5 does not divide 7 but the smallest parts of the other partitions divide their corresponding largest parts.  Therefore, a(6) = 1.

MAPLE

with(numtheory); A234306:=n->n + 1 - tau(2*n); seq(A234306(n), n=1..100);

MATHEMATICA

Table[n + 1 - DivisorSigma[0, 2n], {n, 100}]

PROG

(PARI) a(n) = n + 1 - numdiv(2*n); \\ Michel Marcus, Dec 23 2013

(GAP) List([1..10^4], n->n+1-Tau(2*n)); # Muniru A Asiru, Feb 04 2018

CROSSREFS

Cf. A000005, A066660.

Sequence in context: A308432 A136692 A219194 * A223012 A101452 A019963

Adjacent sequences:  A234303 A234304 A234305 * A234307 A234308 A234309

KEYWORD

nonn,easy

AUTHOR

Wesley Ivan Hurt, Dec 22 2013

STATUS

approved

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Last modified May 25 07:55 EDT 2020. Contains 334585 sequences. (Running on oeis4.)