cp's OEIS Frontend

A375703 Minimum of the n-th maximal run of adjacent (increasing by one at a time) non-perfect-powers.

%I A375703 #10 Aug 29 2024 17:19:19
%S A375703 2,5,10,17,26,28,33,37,50,65,82,101,122,126,129,145,170,197,217,226,
%T A375703 244,257,290,325,344,362,401,442,485,513,530,577,626,677,730,785,842,
%U A375703 901,962,1001,1025,1090,1157,1226,1297,1332,1370,1445,1522,1601,1682,1729
%N A375703 Minimum of the n-th maximal run of adjacent (increasing by one at a time) non-perfect-powers.
%C A375703 Non-perfect-powers A007916 are numbers without a proper integer root.
%F A375703 Numbers k > 0 such that k-1 is a perfect power (A001597) but k is not.
%e A375703 The list of all non-perfect-powers, split into runs, begins:
%e A375703    2   3
%e A375703    5   6   7
%e A375703   10  11  12  13  14  15
%e A375703   17  18  19  20  21  22  23  24
%e A375703   26
%e A375703   28  29  30  31
%e A375703   33  34  35
%e A375703   37  38  39  40  41  42  43  44  45  46  47  48
%e A375703 Row n has length A375702, first a(n), last A375704, sum A375705.
%t A375703 radQ[n_]:=n>1&&GCD@@Last/@FactorInteger[n]==1;
%t A375703 Min/@Split[Select[Range[100],radQ],#1+1==#2&]//Most
%t A375703 - or -
%t A375703 radQ[n_]:=n>1&&GCD@@Last/@FactorInteger[n]==1;
%t A375703 Select[Range[100],radQ[#]&&!radQ[#-1]&]
%Y A375703 For prime numbers we have A045344.
%Y A375703 For nonsquarefree numbers we have A053806, anti-runs A373410.
%Y A375703 For nonprime numbers we have A055670, anti-runs A005381.
%Y A375703 For squarefree numbers we have A072284, anti-runs A373408.
%Y A375703 The anti-run version is A216765 (same as A375703 with 2 exceptions).
%Y A375703 For non-prime-powers we have A373673, anti-runs A120430.
%Y A375703 For prime-powers we have A373676, anti-runs A373575.
%Y A375703 For runs of non-perfect-powers (A007916):
%Y A375703 - length: A375702 = A053289(n+1) - 1.
%Y A375703 - first: A375703 (this)
%Y A375703 - last: A375704
%Y A375703 - sum: A375705
%Y A375703 A001597 lists perfect-powers, differences A053289.
%Y A375703 A007916 lists non-perfect-powers, differences A375706.
%Y A375703 A046933 counts composite numbers between primes.
%Y A375703 A375736 gives lengths of anti-runs of non-prime-powers, sums A375737.
%Y A375703 Cf. A007674, A045542, A375708, A375713, A375714.
%K A375703 nonn
%O A375703 1,1
%A A375703 _Gus Wiseman_, Aug 28 2024