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A378034 First-differences of A378032 (greatest number < prime(n) that is 1 or nonsquarefree).

%I A378034 #5 Nov 19 2024 22:12:20
%S A378034 0,3,0,5,3,4,2,2,8,0,8,4,0,5,7,4,4,4,4,4,4,5,7,8,4,0,4,4,4,14,2,8,0,
%T A378034 12,2,6,6,2,8,4,4,9,3,4,2,10,12,5,3,4,4,4,10,6,5,7,2,6,4,0,12,14,2,4,
%U A378034 4,12,8,8,4,4,4,8,8,6,2,8,8,4,8,8,4,8,4,4
%N A378034 First-differences of A378032 (greatest number < prime(n) that is 1 or nonsquarefree).
%F A378034 a(n) = A378036(prime(n)).
%t A378034 Differences[Table[NestWhile[#-1&,Prime[n],#>1&&SquareFreeQ[#]&],{n,100}]]
%Y A378034 Positions of 0 are A068361.
%Y A378034 The opposite for prime-powers is A377703, differences of A345531.
%Y A378034 For prime-powers we have A377781, differences of A065514.
%Y A378034 The opposite is A377784, differences of A377783 (union A378040).
%Y A378034 First-differences of A378032.
%Y A378034 Restriction of A378036, differences of A378033.
%Y A378034 The opposite for squarefree numbers is A378037, differences of A112926.
%Y A378034 For squarefree numbers we have A378038, differences of A112925.
%Y A378034 The unrestricted opposite is A378039, differences of A120327 (union A162966).
%Y A378034 A000040 lists the primes, differences A001223, seconds A036263.
%Y A378034 A005117 lists the squarefree numbers.
%Y A378034 A013929 lists the nonsquarefree numbers, differences A078147, seconds A376593.
%Y A378034 A061398 counts squarefree numbers between primes (sums A337030), zeros A068360.
%Y A378034 A061399 counts nonsquarefree numbers between primes (sums A378086), zeros A068361.
%Y A378034 A070321 gives the greatest squarefree number up to n.
%Y A378034 A377046 encodes k-differences of nonsquarefree numbers, zeros A377050.
%Y A378034 Cf. A053797, A053806, A072284, A065890, A224363, A377430, A377431.
%Y A378034 Cf. A377047, A377048, A377049, A378082, A378083, A378084.
%K A378034 nonn
%O A378034 1,2
%A A378034 _Gus Wiseman_, Nov 18 2024