cp's OEIS Frontend

A375928 Positions of adjacent non-prime-powers (exclusive) differing by more than 1.

%I A375928 #7 Sep 13 2024 06:53:06
%S A375928 1,2,3,4,6,7,10,11,12,13,14,18,21,22,25,26,29,34,35,37,39,42,43,48,49,
%T A375928 50,55,62,65,66,69,70,73,80,83,84,86,91,92,101,102,107,112,115,116,
%U A375928 119,124,125,134,135,138,139,150,161,164,165,168,173,174,175,182
%N A375928 Positions of adjacent non-prime-powers (exclusive) differing by more than 1.
%F A375928 The inclusive version is a(n+1) - 1.
%e A375928 The non-prime-powers (exclusive) are 1, 6, 10, 12, 14, 15, 18, 20, ... which increase by more than 1 after positions 1, 2, 3, 4, 6, 7, ...
%t A375928 ce=Select[Range[100],!PrimePowerQ[#]&];
%t A375928 Select[Range[Length[ce]-1],!ce[[#+1]]==ce[[#]]+1&]
%Y A375928 For prime-powers inclusive (A000961) we have A376163, differences A373672.
%Y A375928 For nonprime numbers (A002808) we have A014689, differences A046933.
%Y A375928 First differences are A110969.
%Y A375928 The complement is A375713.
%Y A375928 For non-perfect-powers we have A375714, complement A375740.
%Y A375928 The complement for prime-powers (exclusive) is A375734, differences A373671.
%Y A375928 The complement for nonprime numbers is A375926, differences A373403.
%Y A375928 A000040 lists the prime numbers, differences A001223.
%Y A375928 A000961 lists prime-powers (inclusive), differences A057820.
%Y A375928 A007916 lists non-perfect-powers, differences A375706.
%Y A375928 A024619 lists non-prime-powers (inclusive), differences A375735.
%Y A375928 A246655 lists prime-powers (exclusive), differences A174965.
%Y A375928 A361102 lists non-prime-powers (exclusive), differences A375708.
%Y A375928 Cf. A006549, A053289, A073783, A093555, A120430, A176246, A251092.
%K A375928 nonn
%O A375928 1,2
%A A375928 _Gus Wiseman_, Sep 12 2024