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A184830 a(n) = largest k such that A000961(n+1) = A000961(n) + (A000961(n) mod k), or 0 if no such k exists. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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.

LINKS

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

EXAMPLE

For n = 1 we have A000961(1) = 1, A000961(2) = 2; there is no k such that 2 - 1 = 1 = (1 mod k), hence a(1) = 0.

For n = 3 we have A000961(3) = 3, A000961(4) = 4; 2 is the largest k such that 4 - 3 = 1 = (3 mod k), hence a(3) = 2; a(3) = 3 - 1 = 2.

For n = 24 we have A000961(24) = 49, A000961(25) = 53; 45 is the largest k such that 53 - 49 = 4 = (49 mod k), hence a(24) = 45; a(24) = 49 - 4 = 45.

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

CROSSREFS

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

Sequence in context: A187262 A117670 A181695 * A025499 A022474 A194189

Adjacent sequences:  A184827 A184828 A184829 * A184831 A184832 A184833

KEYWORD

nonn,easy

AUTHOR

Rémi Eismann, Jan 23 2011

STATUS

approved

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Last modified March 28 15:52 EDT 2017. Contains 284243 sequences.