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A378036 First differences of A378033 (greatest positive integer < n that is 1 or nonsquarefree).

%I A378036 #11 Jan 28 2025 20:51:46
%S A378036 0,0,3,0,0,0,4,1,0,0,3,0,0,0,4,0,2,0,2,0,0,0,4,1,0,2,1,0,0,0,4,0,0,0,
%T A378036 4,0,0,0,4,0,0,0,4,1,0,0,3,1,1,0,2,0,2,0,2,0,0,0,4,0,0,3,1,0,0,0,4,0,
%U A378036 0,0,4,0,0,3,1,0,0,0,4,1,0,0,3,0,0,0,4,0,2,0,2,0,0,0,4,0,2,1,1,0,0,0,4,0,0,0,4
%N A378036 First differences of A378033 (greatest positive integer < n that is 1 or nonsquarefree).
%H A378036 Antti Karttunen, <a href="/A378036/b378036.txt">Table of n, a(n) for n = 1..65539</a>
%F A378036 a(prime(n)) = A378034(n).
%t A378036 Differences[Table[NestWhile[#-1&,n,#>1&&SquareFreeQ[#]&],{n,100}]]
%o A378036 (PARI)
%o A378036 A378033(n) = if(n<=3, 1, forstep(k=n, 0, -1, if(!issquarefree(k), return(k))));
%o A378036 A378036(n) = (A378033(1+n)-A378033(n)); \\ _Antti Karttunen_, Jan 28 2025
%Y A378036 Positions of 0 are A005117 - 1, complement A013929 - 1.
%Y A378036 Sums for squarefree numbers are A070321 (restriction A112925).
%Y A378036 The restricted opposite is A377784, differences of A377783 (union A378040).
%Y A378036 First-differences of A378033.
%Y A378036 The restriction is A378034, differences of A378032.
%Y A378036 The restricted opposite for squarefree is A378037, differences of A112926.
%Y A378036 The opposite is A378039, differences of A120327 (union A162966).
%Y A378036 For squarefree numbers we have A378085, restriction A378038.
%Y A378036 The opposite for squarefree is A378087, differences of A067535.
%Y A378036 A000040 lists the primes, differences A001223, seconds A036263.
%Y A378036 A005117 lists the squarefree numbers, differences A076259, seconds A376590.
%Y A378036 A013929 lists the nonsquarefree numbers, differences A078147, seconds A376593.
%Y A378036 A061398 counts squarefree numbers between primes (sums A337030), zeros A068360.
%Y A378036 A061399 counts nonsquarefree numbers between primes (sums A378086), zeros A068361.
%Y A378036 A377046 encodes k-differences of nonsquarefree numbers, zeros A377050.
%Y A378036 Cf. A053797, A053806, A065514, A377047, A377048, A377049, A377703, A378082, A378083, A378084.
%K A378036 nonn
%O A378036 1,3
%A A378036 _Gus Wiseman_, Nov 18 2024
%E A378036 Data section extended to a(107) by _Antti Karttunen_, Jan 28 2025