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A373197 Sum of all squarefree numbers from prime(n) to prime(n+1) - 1.

%I A373197 #8 Jun 01 2024 14:29:44
%S A373197 2,3,11,17,11,42,17,62,49,59,133,114,83,89,98,223,59,254,206,71,302,
%T A373197 161,341,462,97,203,314,107,330,824,386,398,275,856,149,460,635,494,
%U A373197 337,702,179,1294,191,582,197,1635,1950,449,227,690,943,239,983,1013,1036
%N A373197 Sum of all squarefree numbers from prime(n) to prime(n+1) - 1.
%e A373197 This is the sequence of row sums of A005117 treated as a triangle with row-lengths A373198:
%e A373197    2
%e A373197    3
%e A373197    5   6
%e A373197    7  10
%e A373197   11
%e A373197   13  14  15
%e A373197   17
%e A373197   19  21  22
%e A373197   23  26
%e A373197   29  30
%e A373197   31  33  34  35
%e A373197   37  38  39
%e A373197   41  42
%e A373197   43  46
%e A373197   47  51
%e A373197   53  55  57  58
%t A373197 Table[Total[Select[Range[Prime[n],Prime[n+1]-1],SquareFreeQ]],{n,15}]
%Y A373197 Counting all numbers (not just squarefree) gives A371201.
%Y A373197 For the sectioning of A005117 (squarefree between prime):
%Y A373197 - sum is A373197 (this sequence)
%Y A373197 - length is A373198 = A061398 - 1
%Y A373197 - min is A000040
%Y A373197 - max is A112925, opposite A112926
%Y A373197 For squarefree numbers between powers of two:
%Y A373197 - sum is A373123
%Y A373197 - length is A077643, partial sums A143658
%Y A373197 - min is A372683, delta A373125, indices A372540, firsts of A372475
%Y A373197 - max is A372889, delta A373126
%Y A373197 For primes between powers of two:
%Y A373197 - sum is A293697 (except initial terms)
%Y A373197 - length is A036378
%Y A373197 - min is A104080 or A014210, indices A372684 (firsts of A035100)
%Y A373197 - max is A014234, delta A013603
%Y A373197 Cf. A372473 (firsts of A372472), A372541 (firsts of A372433).
%Y A373197 Cf. A046933, A049093, A049094, A076259, A077641.
%K A373197 nonn
%O A373197 1,1
%A A373197 _Gus Wiseman_, May 29 2024