A082023 - OEIS

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A082023

Number of partitions of n into 2 parts which are not relatively prime.

0, 0, 0, 0, 1, 0, 2, 0, 2, 1, 3, 0, 4, 0, 4, 3, 4, 0, 6, 0, 6, 4, 6, 0, 8, 2, 7, 4, 8, 0, 11, 0, 8, 6, 9, 5, 12, 0, 10, 7, 12, 0, 15, 0, 12, 10, 12, 0, 16, 3, 15, 9, 14, 0, 18, 7, 16, 10, 15, 0, 22, 0, 16, 13, 16, 8, 23, 0, 18, 12, 23, 0, 24, 0, 19, 17, 20, 8, 27, 0, 24, 13, 21, 0, 30, 10, 22

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OFFSET

0,7

COMMENTS

a(p) = 0 if p is prime.

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..16384

FORMULA

a(0) = 0; and for n >= 1, a(n) = floor((n-phi(n))/2), where phi(n)=A000010(n) is Euler's totient function. - Dean Hickerson, Apr 22 2003. Clarified by Antti Karttunen, Oct 30 2017

EXAMPLE

a(14) = 4 and the partitions are (12,2), (10,4), (8,6) and (7,7).

a(13) = 0 as for all r + s = 13, r > 0, s > 0, gcd(r,s) = 1.

MATHEMATICA

Array[Floor[(# - EulerPhi[#])/2] &, 87, 0] (* or *)

Table[-1 + Boole[n == 1] + Count[IntegerPartitions[n, 2], _?(! CoprimeQ @@ # &)], {n, 0, 86}] (* Michael De Vlieger, Oct 30 2017 *)

PROG

(PARI) A082023(n) = if(0==n, n, ((n-eulerphi(n))\2)); \\ Antti Karttunen, Oct 30 2017

CROSSREFS

Cf. A000010, A082024.

Sequence in context: A055136 A074397 A345039 * A349438 A078152 A339242

Adjacent sequences: A082020 A082021 A082022 * A082024 A082025 A082026