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

Author

Leroy Quet, May 14 2006

Keywords

• nonn
• look

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

Crossrefs

Cf. A064814.

Programs

Mathematica

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

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

Extensions

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