cp's OEIS Frontend

A373412 Sum of the n-th maximal antirun of nonsquarefree numbers differing by more than one.

%I A373412 #6 Jun 07 2024 08:04:43
%S A373412 12,99,52,180,93,49,335,279,156,629,99,540,237,245,125,521,567,450,
%T A373412 963,340,347,728,1386,1080,1637,243,244,1511,1610,555,852,1171,2142,
%U A373412 960,985,1689,343,1042,351,1068,724,732,1116,1905,1980,2898,424,2161,3150,2339
%N A373412 Sum of the n-th maximal antirun of nonsquarefree numbers differing by more than one.
%C A373412 The length of this antirun is given by A373409.
%C A373412 An antirun of a sequence (in this case A013929) is an interval of positions at which consecutive terms differ by more than one.
%H A373412 Gus Wiseman, <a href="/A373403/a373403.txt">Four statistics for runs and antiruns of prime, nonprime, squarefree, and nonsquarefree numbers</a>
%e A373412 Row-sums of:
%e A373412    4   8
%e A373412    9  12  16  18  20  24
%e A373412   25  27
%e A373412   28  32  36  40  44
%e A373412   45  48
%e A373412   49
%e A373412   50  52  54  56  60  63
%e A373412   64  68  72  75
%e A373412   76  80
%e A373412   81  84  88  90  92  96  98
%e A373412   99
%t A373412 Total/@Split[Select[Range[100],!SquareFreeQ[#]&],#1+1!=#2&]//Most
%Y A373412 The partial sums are a subset of A329472.
%Y A373412 Functional neighbors: A068781, A373404, A373405, A373409, A373410, A373411, A373414.
%Y A373412 A005117 lists the squarefree numbers, first differences A076259.
%Y A373412 A013929 lists the nonsquarefree numbers, first differences A078147.
%Y A373412 Cf. A025157, A049093, A049094, A061399, A101836, A112925, A143658, A294242, A350842, A372683, A373197.
%K A373412 nonn
%O A373412 1,1
%A A373412 _Gus Wiseman_, Jun 06 2024