cp's OEIS Frontend

A375737 Sum of the n-th maximal anti-run of adjacent (increasing by more than one at a time) non-perfect-powers.

%I A375737 #5 Sep 11 2024 10:07:21
%S A375737 2,8,6,17,11,12,13,14,32,18,19,20,21,22,23,78,29,30,64,34,72,38,39,40,
%T A375737 41,42,43,44,45,46,47,98,51,52,53,54,55,56,57,58,59,60,61,62,128,66,
%U A375737 67,68,69,70,71,72,73,74,75,76,77,78,79,162,83,84,85,86,87
%N A375737 Sum of the n-th maximal anti-run of adjacent (increasing by more than one at a time) non-perfect-powers.
%C A375737 Non-perfect-powers (A007916) are numbers with no proper integer roots.
%C A375737 An anti-run of a sequence is an interval of positions at which consecutive terms differ by more than one.
%e A375737 The initial anti-runs are the following, whose sums are a(n):
%e A375737   (2)
%e A375737   (3,5)
%e A375737   (6)
%e A375737   (7,10)
%e A375737   (11)
%e A375737   (12)
%e A375737   (13)
%e A375737   (14)
%e A375737   (15,17)
%e A375737   (18)
%e A375737   (19)
%e A375737   (20)
%e A375737   (21)
%e A375737   (22)
%e A375737   (23)
%e A375737   (24,26,28)
%t A375737 radQ[n_]:=n>1&&GCD@@Last/@FactorInteger[n]==1;
%t A375737 Total/@Split[Select[Range[100],radQ],#1+1!=#2&]//Most
%Y A375737 For nonprime numbers we have A373404, runs A054265.
%Y A375737 For squarefree numbers we have A373411, runs A373413.
%Y A375737 For nonsquarefree numbers we have A373412, runs A373414.
%Y A375737 For prime-powers we have A373576, runs A373675.
%Y A375737 For non-prime-powers we have A373679, runs A373678.
%Y A375737 For anti-runs of non-perfect-powers:
%Y A375737 - length: A375736
%Y A375737 - first: A375738
%Y A375737 - last: A375739
%Y A375737 - sum: A375737 (this)
%Y A375737 For runs of non-perfect-powers:
%Y A375737 - length: A375702
%Y A375737 - first: A375703
%Y A375737 - last: A375704
%Y A375737 - sum: A375705
%Y A375737 A001597 lists perfect-powers, differences A053289.
%Y A375737 A007916 lists non-perfect-powers, differences A375706.
%Y A375737 Cf. A007674, A045542, A046933, A053797, A216765, A251092, A373403, A375714.
%K A375737 nonn
%O A375737 1,1
%A A375737 _Gus Wiseman_, Sep 10 2024