A118310 a(n) = gcd(n,m(n)), where m(n) is the n-th nonprime positive integer (1 or composite).

1, 2, 3, 4, 1, 2, 1, 2, 3, 2, 1, 4, 1, 2, 3, 1, 1, 9, 1, 10, 1, 11, 1, 1, 1, 2, 3, 4, 1, 2, 1, 2, 3, 1, 5, 3, 1, 2, 1, 8, 1, 2, 1, 2, 9, 2, 1, 6, 1, 1, 1, 4, 1, 3, 1, 7, 3, 2, 1, 2, 1, 1, 1, 1, 1, 6, 1, 4, 3, 2, 1, 24, 1, 1, 25, 2, 1, 3, 1, 4, 1, 1, 1, 6, 5, 2, 3, 2, 1, 30, 1, 2, 3, 2, 5, 6, 1, 1, 1, 4, 1, 2, 1

Offset

1,2

Comments

For n >= 1, a(n+1) = gcd(n+1,c(n)), where c(n) is the n-th composite.

First occurrence of k: 1, 2, 3, 4, 35, 48, 56, 40, 18, 20, 22, 120, 130, 140, 375, ..., . - Robert G. Wilson v

Question: What is the reason for the conspicuous arc-like structures in the scatter plot? - Antti Karttunen, Mar 02 2023

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Mathematica

NonPrime[n_Integer] := FixedPoint[n + PrimePi@# &, n + PrimePi@n]; f[n_] := GCD[n, NonPrime@n]; Array[f, 103] (* Robert G. Wilson v *)

Prog

(PARI) A002808(maxn)= { local(a); a=[4]; for(n=5, maxn, if( !isprime(n), a=concat(a, n); ); ); return(a); } A118310(maxn)= { local(nonppo, a, newa, nonppol); a=[; ]; nonppo=concat(1, A002808(maxn)); nonppol=matsize(nonppo); for(n=1, nonppol[2], newa= gcd(n, nonppo[n]); a=concat(a, newa); ); return(a); } print(A118310(180)); \\ R. J. Mathar
(PARI) A118310(n) = if(1==n, n, my(x=n-1); for(k=2, oo, if(!isprime(k), x--; if(!x, return(gcd(n, k)))))); \\ Antti Karttunen, Mar 02 2023

Crossrefs

Cf. A064814.

Sequence in context: A104412 A195451 A298160 * A073057 A084310 A214063

Adjacent sequences: A118307 A118308 A118309 * A118311 A118312 A118313

Keyword

nonn,look

Author

Leroy Quet, May 14 2006

Extensions

More terms from Robert G. Wilson v and R. J. Mathar, May 16 2006

Status

approved