

A245689


Smallest divisor of n that is greater than the smallest prime not dividing n (A053669(n)).


2



3, 4, 5, 6, 7, 4, 3, 5, 11, 6, 13, 7, 3, 4, 17, 6, 19, 4, 3, 11, 23, 6, 5, 13, 3, 4, 29, 10, 31, 4, 3, 17, 5, 6, 37, 19, 3, 4, 41, 6, 43, 4, 3, 23, 47, 6, 7, 5, 3, 4, 53, 6, 5, 4, 3, 29, 59, 10, 61, 31, 3, 4, 5, 6, 67, 4, 3, 5, 71, 6, 73, 37, 3, 4, 7, 6, 79
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OFFSET

3,1


COMMENTS

Sequence is similar to A126800 but differs for the first time at n = 30 and thereafter at n = 30k, where k = 3, 5, 7, 9, 11, 13, 14, 15 ... The generating function for k is not known.
The sequence starts at n = 3 as there are no qualifying divisors for n = 1 or n = 2.


LINKS

K. Spage, Table of n, a(n) for n = 3..1000


FORMULA

a(n) = n if n is an odd prime.


EXAMPLE

For n = 30 the smallest prime not dividing n is 7 and the smallest divisor of 30 that is greater than 7 is 10, so a(30) = 10.


MAPLE

a:= proc(n)
uses numtheory;
local F, p;
if n::odd then p:= 2
else
F:= map(pi, factorset(n));
p:= ithprime(min(map(`+`, F, 1) minus F));
fi;
min(select(`>`, divisors(n), p));
end proc:
seq(a(n), n=3..100); # Robert Israel, Jul 31 2014


PROG

(PARI) A053669(n)={forprime(p=2, , if(n%p, return(p)))}
A245689(n) ={my(c=A053669(n)+1); while(n%c, c++); c}


CROSSREFS

Cf. A053669, A245690.
Sequence in context: A049267 A111608 A126800 * A182258 A067628 A168093
Adjacent sequences: A245686 A245687 A245688 * A245690 A245691 A245692


KEYWORD

nonn


AUTHOR

K. Spage, Jul 29 2014


STATUS

approved



