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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 6 06:19 EST 2022. Contains 358595 sequences. (Running on oeis4.)