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A373679 Sums of maximal antiruns of non-prime-powers.

%I A373679 #6 Jun 17 2024 22:44:14
%S A373679 43,53,21,163,34,35,74,39,126,45,144,51,106,55,56,57,180,128,134,69,
%T A373679 216,75,76,77,324,85,86,87,178,91,92,93,94,95,194,99,306,105,324,111,
%U A373679 226,115,116,117,118,119,242,123,379,262,133,134,135,414,141,142,143
%N A373679 Sums of maximal antiruns of non-prime-powers.
%C A373679 An antirun of a sequence (in this case A361102) is an interval of positions at which consecutive terms differ by more than one.
%H A373679 Gus Wiseman, <a href="/A373403/a373403.txt">Four statistics for runs and antiruns of prime, nonprime, squarefree, and nonsquarefree numbers</a>.
%e A373679 The maximal antiruns of non-prime-powers begin:
%e A373679    1   6  10  12  14
%e A373679   15  18  20
%e A373679   21
%e A373679   22  24  26  28  30  33
%e A373679   34
%e A373679   35
%e A373679   36  38
%e A373679   39
%e A373679   40  42  44
%e A373679   45
%e A373679   46  48  50
%e A373679   51
%e A373679   52  54
%e A373679   55
%e A373679   56
%e A373679   57
%e A373679   58  60  62
%e A373679   63  65
%t A373679 Total/@Split[Select[Range[100],!PrimePowerQ[#]&],#1+1!=#2&]//Most
%Y A373679 See link for composite, prime, nonsquarefree, and squarefree runs/antiruns.
%Y A373679 Prime-power runs: A373675, min A373673, max A373674, length A174965.
%Y A373679 Non-prime-power runs: A373678, min A373676, max A373677, length A110969.
%Y A373679 Prime-power antiruns: A373576, min A120430, max A006549, length A373671.
%Y A373679 Non-prime-power antiruns: A373679 (this sequence), min A373575, max A255346, length A373672.
%Y A373679 A000040 lists the primes, differences A001223.
%Y A373679 A000961 lists all powers of primes. A246655 lists just prime-powers.
%Y A373679 A025528 counts prime-powers up to n.
%Y A373679 A057820 gives first differences of consecutive prime-powers, gaps A093555.
%Y A373679 A356068 counts non-prime-powers up to n.
%Y A373679 A361102 lists all non-prime-powers (A024619 if not including 1).
%Y A373679 Cf. A001359, A014963, A027833, A029707, A038664, A054265, A067774, A071148, A251092, A371201, A373401, A373669.
%K A373679 nonn
%O A373679 1,1
%A A373679 _Gus Wiseman_, Jun 17 2024