A082023 - OEIS

%I #11 Oct 30 2017 17:56:42

%S 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,

%T 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,

%U 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

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

%C a(p) = 0 if p is prime.

%H Antti Karttunen, <a href="/A082023/b082023.txt">Table of n, a(n) for n = 0..16384</a>

%F 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

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

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

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

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

%o (PARI) A082023(n) = if(0==n,n,((n-eulerphi(n))\2)); \\ _Antti Karttunen_, Oct 30 2017

%Y Cf. A000010, A082024.

%K nonn

%O 0,7

%A _Amarnath Murthy_, Apr 07 2003

%E More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 20 2003