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A240603
Numbers that are the sum of two successive squarefree numbers.
2
3, 5, 8, 11, 13, 17, 21, 24, 27, 29, 32, 36, 40, 43, 45, 49, 55, 59, 61, 64, 67, 69, 72, 75, 77, 80, 83, 85, 89, 93, 98, 104, 108, 112, 115, 117, 120, 123, 127, 131, 133, 136, 139, 141, 144, 147, 151, 155, 157, 161, 165, 168, 171, 173, 176, 180, 184, 187, 189, 192, 198, 203
OFFSET
1,1
LINKS
FORMULA
a(n) = A005117(n) + A005117(n+1).
EXAMPLE
3 + 5 = 8, so 8 is in the sequence.
5 + 6 = 11, so 11 is in the sequence.
Although 12 can be expressed as a sum of two squarefree numbers, none of those sums (1 + 11, 2 + 10, 5 + 7, 6 + 6) involve successive squarefree numbers. Therefore 12 is not in the sequence.
MAPLE
N:= 1000; # to get entries up to approximately 2*N
SF:= select(numtheory:-issqrfree, [$1..N]):
seq(SF[i]+SF[i+1], i=1..nops(SF)-1); # Robert Israel, Jun 08 2014
MATHEMATICA
Abs[Differences[Select[Range[100], MoebiusMu[#] != 0 &] * (-1)^Range[61]]] (* Alonso del Arte, Jun 08 2014 *)
Total/@Partition[Select[Range[200], SquareFreeQ], 2, 1] (* Harvey P. Dale, Oct 09 2018 *)
PROG
(PARI) lista(nn) = {v = vector(nn, i, i); vsqf = select(n->issquarefree(n), v); for (i=1, #vsqf-1, print1(vsqf[i] + vsqf[i+1], ", "); ); } \\ Michel Marcus, May 31 2014
CROSSREFS
Sequence in context: A022850 A008576 A047622 * A079392 A185723 A022852
KEYWORD
nonn,easy
AUTHOR
STATUS
approved