A105604 Sylvester dividends for Jacobsthal numbers.

1, 1, 1, 1, 1, 3, 1, 5, 3, 11, 1, 105, 1, 43, 33, 85, 1, 1197, 1, 1705, 129, 683, 1, 23205, 11, 2731, 171, 27305, 1, 2370291, 1, 21845, 2049, 43691, 473, 5679765, 1, 174763, 8193, 5941925, 1, 621456339, 1, 6990505, 622611, 2796203, 1, 1437248085, 43, 346729141, 131073, 111848105, 1, 22861753173, 7513, 1521134245

Offset: 1

Author

Paul Barry, Apr 15 2005

Keywords

• easy
• nonn

Comments

Divide each Jacobsthal number by its primitive part.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..4096

Crossrefs

Cf. A001045, A105603.

Programs

PARI

A001045(n) = ((2^n - ((-1)^n)) / 3);
A105603(n) = if(1==n,n,(-1)^eulerphi(n)*polcyclo(n, -2)); \\ After Wolfdieter Lang's formula in that entry.
A105604(n) = (A001045(n)/A105603(n)); \\ Antti Karttunen, Nov 01 2017

Formula

a(n) = A001045(n)/A105603(n).

Extensions

More terms from Antti Karttunen, Nov 01 2017