

A098699


Antiderivative of n: or the first occurrence of n in A003415, or zero if impossible.


9



1, 2, 0, 0, 4, 6, 9, 10, 15, 14, 21, 0, 8, 22, 33, 26, 12, 0, 65, 34, 51, 18, 57, 0, 20, 46, 69, 27, 115, 0, 161, 30, 16, 62, 93, 0, 155, 0, 217, 45, 111, 42, 185, 82, 24, 50, 129, 0, 44, 94, 141, 63, 235, 0, 329, 75, 52, 0, 265, 70, 36, 66, 177, 122, 183, 0, 305, 0, 40, 134
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OFFSET

0,2


COMMENTS

With Goldbach's conjecture, any even integer n = 2k > 2 can be written as sum of two primes, n = p + q, and therefore admits N = pq as (not necessarily smallest) antiderivative, so a(2k) > 0, and a(2k) <= pq <= k^2. [Remark inspired by L. Polidori.]  M. F. Hasler, Apr 09 2015


LINKS

T. D. Noe, Table of n, a(n) for n = 0..5000


FORMULA

a(n) = n for { 4, 27, 3125, 823543, ... } = { p^p; p prime } = A051674.


MATHEMATICA

a[1] = 0; a[n_] := Block[{f = Transpose[ FactorInteger[ n]]}, If[ PrimeQ[n], 1, Plus @@ (n*f[[2]]/f[[1]])]]; b = Table[0, {70}]; b[[1]] = 1; Do[c = a[n]; If[c < 70 && b[[c + 1]] == 0, b[[c + 1]] = n], {n, 10^3}]; b


PROG

(PARI) A098699(n)=for(k=1, (n\2)^2+2, A003415(k)==n&&return(k)) \\ M. F. Hasler, Apr 09 2015


CROSSREFS

Cf. A003415, A051674, zeros in A098700.
Sequence in context: A284611 A282551 A056676 * A021837 A236934 A155719
Adjacent sequences: A098696 A098697 A098698 * A098700 A098701 A098702


KEYWORD

nonn


AUTHOR

Robert G. Wilson v, Sep 21 2004


STATUS

approved



