cp's OEIS Frontend

A319179 Number of integer partitions of n that are relatively prime but not aperiodic. Number of integer partitions of n that are aperiodic but not relatively prime.

%I A319179 #4 Sep 15 2018 15:48:07
%S A319179 0,1,1,1,1,2,1,3,2,6,1,9,1,14,7,17,1,32,1,36,15,55,1,77,6,100,27,121,
%T A319179 1,200,1,209,56,296,19,403,1,489,101,596,1,885,1,947,192,1254,1,1673,
%U A319179 14,1979,297,2336,1,3300,60,3594,490,4564,1,5988,1,6841,800
%N A319179 Number of integer partitions of n that are relatively prime but not aperiodic. Number of integer partitions of n that are aperiodic but not relatively prime.
%C A319179 An integer partition is aperiodic if its multiplicities are relatively prime.
%e A319179 The a(12) = 9 integer partitions that are relatively prime but not aperiodic:
%e A319179   (5511),
%e A319179   (332211), (333111), (441111),
%e A319179   (22221111), (33111111),
%e A319179   (222111111),
%e A319179   (2211111111),
%e A319179   (111111111111).
%e A319179 The a(12) = 9 integer partitions that are aperiodic but not relatively prime:
%e A319179   (12),
%e A319179   (8,4), (9,3), (10,2),
%e A319179   (6,3,3), (6,4,2), (8,2,2),
%e A319179   (6,2,2,2),
%e A319179   (4,2,2,2,2).
%t A319179 Table[Length[Select[IntegerPartitions[n],And[GCD@@#==1,GCD@@Length/@Split[#]>1]&]],{n,30}]
%Y A319179 Cf. A000837, A018783, A047966, A100953, A305563, A319149, A319160, A319162, A319164.
%K A319179 nonn
%O A319179 1,6
%A A319179 _Gus Wiseman_, Sep 12 2018