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

1,1

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 n-th composite), A056608 (smallest divisor of n-th 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