A240603 Numbers that are the sum of two successive squarefree numbers.

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

Robert Israel, Table of n, a(n) for n = 1..10000

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

Cf. A001043, A005117.

Sequence in context: A022850 A008576 A047622 * A079392 A185723 A022852

Adjacent sequences: A240600 A240601 A240602 * A240604 A240605 A240606

Keyword

nonn,easy

Author

Juri-Stepan Gerasimov, May 30 2014

Status

approved