A354999 a(n) = n divided by the smallest divisor d of n for which A344005(d) = A344005(n), where A344005(n) is the smallest positive integer m such that n divides m*(m+1).

1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 3, 1, 2, 1, 1, 1, 2, 1, 4, 3, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 4, 1, 2, 3, 1, 1, 6, 1, 1, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 5, 7, 3, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 3, 1, 1, 6, 1, 5, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 2, 1, 4, 1, 2, 1, 1, 3

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Formula

a(n) = n / A354998(n).

Mathematica

Module[{m = 1}, While[! Divisible[m*(m + 1), n], m++]; m]; a[n_] := Module[{sn = s[n], ds = Divisors[n]}, Do[If[s[d] == sn, Return[n/d]], {d, ds}]]; Array[a, 100] (* Amiram Eldar, Jun 17 2022 *)

Prog

(PARI)
A344005(n) = for(m=1, oo, if((m*(m+1))%n==0, return(m))); \\ From A344005
A354999(n) = { my(x=A344005(n)); fordiv(n, d, if(A344005(d)==x, return(n/d))); };

Crossrefs

Cf. A344005, A354991, A354992, A354994 (positions of 1's), A354998.

Cf. also A344759, A346089.

Sequence in context: A076398 A086257 A161098 * A136177 A212178 A322818

Adjacent sequences: A354996 A354997 A354998 * A355000 A355001 A355002

Keyword

nonn

Author

Antti Karttunen, Jun 17 2022

Status

approved