A227006 Numbers k such that k-1 is not squarefree or a prime divisor of k-1 is in the sequence.

5, 6, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75

Offset: 1

Author

José María Grau Ribas, Jun 27 2013

Keywords

• nonn
• easy

Comments

The sequence is defined recursively. The complement of A227007.

Links

• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A227007.

Programs

Mathematica

Needs["NumberTheory`NumberTheoryFunctions`"];Property[2] = False; Property[{}] = False; Property[n_] := Property[n] = If[ListQ[n],Property[n[[1, 1]]] || Property[Rest[n]], SquareFreeQ[n - 1] == False || Property[fa[n - 1]]]; Select[1 + Range[100], Property]

PARI

is(n)=if(n<7,return(n>4)); if(n>1807 || !issquarefree(n-1), return(1)); fordiv(n-1,d,if(isprime(d) && is(d), return(1))); 0 \\ Charles R Greathouse IV, Nov 13 2013

Formula

a(n) = n + 16 for n > 1791. - Charles R Greathouse IV, Jun 27 2013

Extensions

Definition corrected by Charles R Greathouse IV, Nov 13 2013