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A373576 Sums of maximal antiruns of prime-powers.

%I A373576 #8 Jun 18 2024 21:06:57
%S A373576 2,3,4,12,8,49,171,2032,5157,3997521,199713082,561678378,10122001905,
%T A373576 109934112352390774
%N A373576 Sums of maximal antiruns of prime-powers.
%C A373576 An antirun of a sequence (in this case A246655) is an interval of positions at which consecutive terms differ by more than one.
%H A373576 Gus Wiseman, <a href="/A373403/a373403.txt">Four statistics for runs and antiruns of prime, nonprime, squarefree, and nonsquarefree numbers</a>.
%e A373576 The maximal antiruns of powers of primes begin:
%e A373576    2
%e A373576    3
%e A373576    4
%e A373576    5   7
%e A373576    8
%e A373576    9  11  13  16
%e A373576   17  19  23  25  27  29  31
%t A373576 Total/@Split[Select[Range[1000],PrimePowerQ],#1+1!=#2&]//Most
%Y A373576 See link for composite, prime, nonsquarefree, and squarefree runs/antiruns.
%Y A373576 Prime-power runs: A373675, min A373673, max A373674, length A174965.
%Y A373576 Non-prime-power runs: A373678, min A373676, max A373677, length A110969.
%Y A373576 Prime-power antiruns: A373576 (this sequence), min A120430, max A006549, length A373671.
%Y A373576 Non-prime-power antiruns: A373679, min A373575, max A255346, length A373672.
%Y A373576 A000040 lists the primes, differences A001223.
%Y A373576 A000961 lists all powers of primes. A246655 lists just prime-powers.
%Y A373576 A025528 counts prime-powers up to n.
%Y A373576 A057820 gives first differences of consecutive prime-powers, gaps A093555.
%Y A373576 A356068 counts non-prime-powers up to n.
%Y A373576 A361102 lists all non-prime-powers (A024619 if not including 1).
%Y A373576 Cf. A001359, A014963, A027833, A029707, A038664, A067774, A251092, A293697, A371201, A373401, A373669.
%K A373576 nonn,more
%O A373576 1,1
%A A373576 _Gus Wiseman_, Jun 17 2024
%E A373576 a(14) from _Giorgos Kalogeropoulos_, Jun 18 2024