0,3

Comment from Marc LeBrun (mlb(AT)well.com), Dec 12, 2001: Define a "numbral arithmetic" by replacing addition with binary bitwise inclusive-OR (so that [3] + [5] = [7] etc) and multiplication becomes shift-&-OR instead of shift-&-add (so that [3] * [3] = [7] etc). [d] divides [n] means there exists an [e] with [d] * [e] = [n]. For example the six divisors of [14] are [1], [2], [3], [6], [7] and [14]. Then it appears that this sequence gives the number of proper divisors of [2^n-1]. Conjecture confirmed by Richard Schroeppel (rschroe(AT)sandia.gov), Dec 14, 2001

The number of "prime endofunctions" on n points, meaning the cardinality of the subset of the A001372(n) mappings (or mapping patterns) up to isomorphism from n (unlabeled) points to themselves (endofunctions) which are neither the sum of prime endofunctions (i.e. whose disjoint connected components are prime endofunctions) nor the categorical product of prime endofunctions. The n for which a(n) is prime (n such that the number of prime endofunctions on n points is itself prime) are 2, 4, 5, 6, 9, 13, 19, ... - Jonathan Vos Post (jvospost3(AT)gmail.com), Nov 19 2006

A. Frosini and S. Rinaldi, On the Sequence A079500 and Its Combinatorial Interpretations, Journal of Integer Sequences, Vol. 9 (2006), Article 06.3.1.

G.f.: Sum_{k>0} x^k*(1-x^k)/(1-2*x+x^(k+1)). - Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 25 2003

a(m) = Sum_{ n=2..m+1 } Fn(m) where Fn is a Fibonacci n-step number (Fibonacci, Tetranacci, etc.) indexed as in A000045, A000073, A000078. - Gerald McGarvey (Gerald.McGarvey(AT)comcast.net), Sep 25 2004

Cf. A007059.

Cf. A000312, A001372, A002861, A006961, A001373, A054050, A054745, A125024.

Sequence in context: A003116 A165648 A078038 this_sequence A026724 A054163 A036256

Adjacent sequences: A048885 A048886 A048887 this_sequence A048889 A048890 A048891

nonn

Clark Kimberling (ck6(AT)evansville.edu)