

A161986


a(n) = k+r where k is composite(n) and r is (largest prime divisor of k) mod (smallest prime divisor of k).


3



4, 7, 8, 9, 11, 13, 15, 17, 16, 19, 21, 22, 23, 25, 25, 27, 27, 29, 31, 32, 35, 35, 37, 37, 39, 40, 41, 43, 45, 47, 47, 49, 49, 51, 53, 53, 55, 56, 57, 58, 59, 61, 63, 64, 64, 68, 67, 69, 71, 71, 73, 75, 77, 77, 81, 79, 81, 81, 83, 85, 87, 87, 89, 89, 91, 97, 93, 94, 95, 99, 97
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OFFSET

1,1


COMMENTS

Auxiliary sequence for A161850, which is the subsequence consisting of all terms that are prime.
a(n) = A002808(n)+A161849(n).


LINKS

Bill McEachen, Table of n, a(n) for n = 1..10000


EXAMPLE

n = 1: composite(1) = 4; (largest prime divisor of 4) = (smallest prime divisor 4) = 2; 2 mod 2 = 0. Hence a(1) = 4+0 = 4.
n = 5: composite(5) = 10; (largest prime divisor of 10) = 5; (smallest prime divisor 10) = 2; 5 mod 2 = 1. Hence a(5) = 10+1 = 11.


PROG

(Magma) [ n + D[ #D] mod D[1]: n in [2..100]  not IsPrime(n) where D is PrimeDivisors(n) ];
(PARI) genit(maxx=1000)={ctr=0; arr=List(); forcomposite(k=4, +oo, v=factor(k)[, 1]; r=v[#v]%v[1]; ctr+=1; if(ctr>=maxx, break); listput(arr, k+r)); arr} \\ Bill McEachen, Nov 17 2021


CROSSREFS

Cf. A161850, A002808 (composite numbers), A052369 (largest prime factor of nth composite), A056608 (smallest divisor of nth composite), A161849 (A052369(n) mod A056608(n)).
Sequence in context: A060257 A262874 A309264 * A324940 A020670 A253472
Adjacent sequences: A161983 A161984 A161985 * A161987 A161988 A161989


KEYWORD

nonn


AUTHOR

Klaus Brockhaus, Jun 23 2009


STATUS

approved



