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

Offset: 0

Author

Amarnath Murthy, Apr 07 2003

Keywords

• nonn

Comments

a(p) = 0 if p is prime.

Examples

			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.
		

Links

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

Crossrefs

Cf. A000010, A082024.

Programs

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 *)

PARI

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

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

Extensions

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