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

1,1

Comments

No odd integer has any non-isolated divisors.

Links

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

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

Prog

(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

Crossrefs

Cf. A133780, A133828.

Sequence in context: A281908 A106441 A131836 * A364925 A160651 A230296

Adjacent sequences: A133826 A133827 A133828 * A133830 A133831 A133832

Keyword

nonn

Author

Leroy Quet, Sep 25 2007

Extensions

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

Status

approved