A161850 -id:A161850 - cp's OEIS frontend

A161849 a(n) = A052369(n) mod A056608(n).

0, 1, 0, 0, 1, 1, 1, 2, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 2, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 0, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 1, 1, 2, 1, 1, 1, 2, 1, 4, 1, 1, 0, 1, 1, 2, 1, 2, 1, 1, 6, 1, 1, 1, 4, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 1, 0, 1, 2, 1, 0, 1, 0, 1, 1, 1, 5, 1, 2, 1, 1, 1

Offset: 1

Juri-Stepan Gerasimov, Jun 20 2009

nonn

(Largest prime divisor) modulo (smallest prime divisor) of n-th composite number.

			a(1) = 0 = 2 mod 2;
a(2) = 1 = 3 mod 2;
a(3) = 0 = 2 mod 2;
a(4) = 0 = 3 mod 3;
a(5) = 1 = 5 mod 2.

Cf. A052369, A056608, A002808.

Cf. A161850, A161986. - Klaus Brockhaus, Jun 24 2009

[ D[ #D] mod D[1]: n in [2..140] | not IsPrime(n) where D is PrimeDivisors(n) ]; // Klaus Brockhaus, Jun 24 2009

A002808 := proc(n) option remember; local a; if n = 1 then 4; else for a from procname(n-1)+1 do if not isprime(a) then RETURN(a) : fi; od: fi; end:
A006530 := proc(n) local u: if n=1 then 1 else u:= numtheory[factorset](n): max(seq(u[j], j=1..nops(u))) end if end:
A020639 := proc(n) local u: if n=1 then 1 else u:= numtheory[factorset](n): min(seq(u[j], j=1..nops(u))) end if end:
A052369 := proc(n) A006530(A002808(n)) ; end:
A056608 := proc(n) A020639(A002808(n)) ; end:
A161849 := proc(n) A052369(n) mod A056608(n) ; end: seq(A161849(n),n=1..120) ; # R. J. Mathar, Jun 23 2009

Composite[n_] := FixedPoint[n + PrimePi[#] + 1&, n + PrimePi[n] + 1];
a[n_] := With[{f = FactorInteger[Composite[n]]}, f[[-1, 1]]~Mod~f[[1, 1]]];
Table[a[n], {n, 1, 105}] (* Jean-François Alcover, Oct 15 2023 *)

a(102) corrected by R. J. Mathar, Jun 23 2009

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

Original entry on oeis.org

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

Klaus Brockhaus, Jun 23 2009

nonn

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

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

			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.

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

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)).

[ n + D[ #D] mod D[1]: n in [2..100] | not IsPrime(n) where D is PrimeDivisors(n) ];

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

cp's OEIS Frontend

A161849 a(n) = A052369(n) mod A056608(n).

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