A133829 a(n) = the largest "non-isolated divisor" of 2n. A positive divisor k of n is non-isolated if k-1 or k+1 also divides n.

2, 2, 3, 2, 2, 4, 2, 2, 3, 5, 2, 4, 2, 2, 6, 2, 2, 4, 2, 5, 7, 2, 2, 4, 2, 2, 3, 8, 2, 6, 2, 2, 3, 2, 2, 9, 2, 2, 3, 5, 2, 7, 2, 2, 10, 2, 2, 4, 2, 5, 3, 2, 2, 4, 11, 8, 3, 2, 2, 6, 2, 2, 7, 2, 2, 12, 2, 2, 3, 5, 2, 9, 2, 2, 6, 2, 2, 13, 2, 5, 3, 2, 2, 8, 2, 2, 3, 2, 2, 10, 14, 2, 3, 2, 2, 4, 2, 2, 3

Offset: 1

Author

Leroy Quet, Sep 25 2007

Keywords

• nonn

Comments

No odd integer has any non-isolated divisors.

Links

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

Crossrefs

Cf. A133780, A133828.

Programs

Maple

A133829 := proc(n) local divs,k,i ; divs := sort(convert(numtheory[divisors](2*n),list)) ; for i from 1 to nops(divs) do k := op(-i,divs) ; if k-1 in divs or k+1 in divs then RETURN(k) ; fi ; od: RETURN(0) ; end: seq(A133829(n),n=1..100) ; # R. J. Mathar, Oct 19 2007

PARI

A133829(n) = { n = 2*n; my(m=0); fordiv(n,d,if(!(n%(1+d)) || ((d>1) && !(n%(d-1))), m = max(m,d))); (m); }; \\ Antti Karttunen, Mar 02 2023

Extensions

More terms from R. J. Mathar, Oct 19 2007