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A375705 Sum of the n-th maximal run of adjacent (increasing by one at a time) non-perfect-powers.

%I A375705 #6 Sep 06 2024 14:08:56
%S A375705 5,18,75,164,26,118,102,510,791,1160,1629,2210,369,253,2040,3756,4745,
%T A375705 3914,1764,3978,2994,8720,10421,6003,5984,14459,16820,19425,13446,
%U A375705 8328,25415,28824,32525,36530,40851,45500,50489,55830,37259,23276,67616,74085,80954
%N A375705 Sum of the n-th maximal run of adjacent (increasing by one at a time) non-perfect-powers.
%C A375705 Non-perfect-powers (A007916) are numbers without a proper integer root.
%e A375705 The list of all non-perfect-powers, split into runs, begins:
%e A375705    2   3
%e A375705    5   6   7
%e A375705   10  11  12  13  14  15
%e A375705   17  18  19  20  21  22  23  24
%e A375705   26
%e A375705   28  29  30  31
%e A375705   33  34  35
%e A375705   37  38  39  40  41  42  43  44  45  46  47  48
%e A375705 Row n begins with A375703(n), ends with A375704(n), adds up to a(n), and has length A375702(n).
%t A375705 radQ[n_]:=n>1&&GCD@@Last/@FactorInteger[n]==1;
%t A375705 Total/@Split[Select[Range[100],radQ],#1+1==#2&]//Most
%Y A375705 For nonprime numbers we have A054265, anti-runs A373404.
%Y A375705 For nonsquarefree numbers we have A373414, anti-runs A373412.
%Y A375705 For squarefree numbers we have A373413, anti-runs A373411.
%Y A375705 For prime-powers we have A373675, anti-runs A373576.
%Y A375705 For non-prime-powers we have A373678, anti-runs A373679.
%Y A375705 The anti-run version is A375737, sums of A375736.
%Y A375705 A001597 lists perfect-powers, differences A053289.
%Y A375705 A007916 lists non-perfect-powers, differences A375706.
%Y A375705 A046933 counts composite numbers between primes.
%Y A375705 For runs of non-perfect-powers:
%Y A375705 - length: A375702 = A053289(n+1) - 1
%Y A375705 - first: A375703 (same as A216765 with 2 exceptions)
%Y A375705 - last: A375704 (same as A045542 with 8 removed)
%Y A375705 - sum: A375705 (this)
%Y A375705 Cf. A006093, A006549, A251092, A255346, A371201, A373197, A375708.
%K A375705 nonn
%O A375705 1,1
%A A375705 _Gus Wiseman_, Aug 29 2024