

A045545


a(0) = 1; a(n) = Sum(0 <= k < n and gcd(k,n) = 1; a(k)).


7



1, 1, 1, 2, 3, 7, 8, 22, 32, 66, 91, 233, 263, 729, 1038, 2059, 3119, 7674, 8666, 24014, 32741, 68645, 103219, 252633, 285313, 755681, 1111037, 2292275, 3335374, 8284946, 8570252, 25140144, 36829131, 75778418, 112599875, 262721802
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OFFSET

0,4


COMMENTS

a(n+2)=2*a(n)+a(n+1) if and only if n is the lesser of a pair of twin primes (i.e., n is in A001359).  Benoit Cloitre, Nov 28 2002
Starting with offset 1 = row sums of triangle A143656.  Gary W. Adamson, Aug 28 2008


LINKS

Table of n, a(n) for n=0..35.


FORMULA

Lim sup a(n+1)/a(n) = 3.  Jan Szejko (js248325(AT)students.mimuw.edu.pl), May 29 2010
Equals M * V where M = A054521 is an infinite lower triangular matrix and V = A045545 is a vector starting [1, 1, 2, 3, 7, 8,...]. E.g., a(6) = 8 since the relative primes of 6 are 1 and 5 and a(1) + a(5) = 1 + 7 = 8.  Gary W. Adamson, Jan 13 2007


MATHEMATICA

a[0] = 1; a[n_] := a[n] = Block[{k = 0, s = 0}, While[k < n, If[ GCD[n, k] == 1, s = s + a[k]]; k++ ]; s]; Table[ a[n], {n, 0, 35}] (* Robert G. Wilson v, Jun 09 2006 *)


CROSSREFS

Cf. A023896, A054251, A002033.
Cf. A143656.  Gary W. Adamson, Aug 28 2008
Sequence in context: A137823 A024540 A029785 * A029790 A206725 A129645
Adjacent sequences: A045542 A045543 A045544 * A045546 A045547 A045548


KEYWORD

nonn


AUTHOR

David W. Wilson


STATUS

approved



