A161986 a(n) = k+r where k is composite(n) and r is (largest prime divisor of k) mod (smallest prime divisor of k).

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

Offset: 1

Author

Klaus Brockhaus, Jun 23 2009

Keywords

• nonn

Comments

Auxiliary sequence for A161850, which is the subsequence consisting of all terms that are prime.

a(n) = A002808(n)+A161849(n).

Examples

			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.
		

Links

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

Crossrefs

Cf. A161850, A002808 (composite numbers), A052369 (largest prime factor of n-th composite), A056608 (smallest divisor of n-th composite), A161849 (A052369(n) mod A056608(n)).

Programs

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