A184830 a(n) = largest k such that A000961(n+1) = A000961(n) + (A000961(n) mod k), or 0 if no such k exists.

0, 0, 2, 3, 3, 6, 7, 7, 9, 10, 15, 15, 15, 21, 23, 25, 27, 30, 27, 33, 39, 39, 45, 45, 47, 57, 58, 61, 63, 69, 67, 77, 79, 77, 81, 93, 99, 99, 105, 105, 105, 117, 123, 126, 125, 125, 135, 129, 147, 145, 151, 159, 165, 165, 167, 177, 171, 189, 189, 195

Offset: 1

Author

Rémi Eismann, Jan 23 2011

Keywords

• nonn
• easy

Comments

From the definition, a(n) = A000961(n) - A057820(n) if A000961(n) - A057820(n) > A057820(n), 0 otherwise where A000961 are the prime powers and A057820 are the gaps between prime powers.

Examples

			For n = 1 we have A000961(1) = 1, A000961(2) = 2; for all k >= 2, 2 = 1 + (1 mod k), hence the largest k does not exist and a(1) = 0.
For n = 3 we have A000961(3) = 3, A000961(4) = 4; 2 is the largest k such that 4 = 3 + (3 mod k), hence a(3) = 2.
For n = 24 we have A000961(24) = 49, A000961(25) = 53; 45 is the largest k such that 53 = 49 + (49 mod k), hence a(24) = 45.
		

Links

• Rémi Eismann, Table of n, a(n) for n = 1..9790

Crossrefs

Cf. A000961, A057820, A184829, A184831, A117078, A117563, A001223, A118534.

Programs

Maple

A184830 := proc(n)
    if A000961(n) > 2*A057820(n) then
        A000961(n)-A057820(n) ;
    else
        0;
    end if;
end proc:
seq(A184830(n),n=1..40) ; # R. J. Mathar, Sep 23 2016

Mathematica

nmax = 10000;
ppmax = 12*nmax; (* increase prime power max coef 12 in case of overflow *)
A000961 = Join[{1}, Select[Range[2, ppmax], PrimePowerQ]];
A057820 = Differences[A000961];
a[n_] := If[A000961[[n]] > 2*A057820[[n]], A000961[[n]] - A057820[[n]], 0];
Table[a[n], {n, 1, nmax}] (* Jean-François Alcover, Aug 06 2023 *)