A079274 Number of divisors associated with the cyclic cases within the n-th group of least prime signatures.

1, 0, 3, 4, 14, 18, 65, 82, 253, 378, 953, 1460, 3667, 5480, 12917, 20582, 45130, 71970, 156510, 248020, 524446, 846962, 1733252, 2806484, 5702101, 9186010, 18375867, 29872508, 58760991, 95500008, 186871472, 302966474, 587603027, 956192230, 1836704483, 2988458542

Offset

0,3

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1000

Formula

a(n) = A074141(n) - 2*A074141(n-1) for n > 0 with a(0) = 1.

G.f.: (1 - 2*x)/Product_{k>=1} (1 - (k+1)*x^k). - Andrew Howroyd, Oct 04 2025

Example

The number of divisors doubles each time we create a new "matching" partition by appending "1" to a given partition. Therefore we may write
..1..0..3..4..14..18..65..82..253..378..953...
+ ...2..4.14..36.100.236.602.1368.3242.7240...
= 1..2..7.18..50.118.301.684.1621.3620.8193...

Prog

(PARI) seq(n)={Vec((1 - 2*x)/prod(k=1, n, 1 - (k+1)*x^k + O(x*x^n)))} \\ Andrew Howroyd, Oct 04 2025

Crossrefs

Cf. A074141.

Sequence in context: A297839 A279938 A280331 * A392183 A282421 A282684

Adjacent sequences: A079271 A079272 A079273 * A079275 A079276 A079277

Keyword

easy,nonn

Author

Alford Arnold, Feb 06 2003

Extensions

More terms from Pab Ter (pabrlos(AT)yahoo.com), May 27 2004

Status

approved