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A143615 Triangle A054521 * A000005 as a vector. 5
1, 1, 3, 3, 8, 3, 14, 7, 14, 8, 27, 7, 35, 12, 20, 18, 50, 11, 58, 16, 35, 24, 74, 15, 68, 29, 54, 29, 101, 15, 111, 39, 64, 41, 84, 26, 140, 47, 78, 40, 158, 24, 168, 51, 75, 61, 186, 34, 170, 49, 111, 66, 217, 39, 160, 65, 131, 80, 247, 32, 261, 84, 122, 92, 197, 45, 292, 92, 162, 60, 312, 55, 326, 104, 135, 106, 263, 55, 356, 85, 206 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
FORMULA
Triangle A054521 * A000005 as a vector; where 1's indicate the relative primes of n by rows and A000005 = d(n): (1, 2, 2, 3, 2, 4, 2, 4, 3,...)
a(n) = Sum_{ m=1..n and gcd(n,m)=1 } tau(m), where tau(m)=A000005(m). A211932(n)+a(n) = A006218(n). [Naohiro Nomoto, Aug 05 2012]
EXAMPLE
a(8) = 7 since the relative primes of 8 are (1, 3, 5, 7). (d(1) + d(3) + d(5) + d(7)) = 1 + 2 + 2 + 2). Or, a(8) = 7 = (1, 0, 1, 0, 1, 0, 1, 0) dot (1, 2, 2, 3, 2, 4, 2, 4), where (1, 0, 1, 0, 1, 0, 1, 0) = row 8 of triangle A054521 and d(n) = (1, 2, 2, 3, 2, 4, 2, 4, 3, 4, 2,...).
a(7) = 14 = (1, 1, 1, 1, 1, 1, 0) dot (1, 2, 2, 3, 2, 4, 2) = (d(1) + d(2) + d(3) + d(4) + d(5) + d(6)).
MAPLE
A143615 := proc(n)
local a, m;
a := 0 ;
for m from 1 to n do
if gcd(m, n) = 1 then
a := a+numtheory[tau](m) ;
end if;
end do:
a ;
end proc: # R. J. Mathar, Aug 08 2012
CROSSREFS
Sequence in context: A212809 A294643 A029614 * A199337 A279789 A249389
KEYWORD
nonn
AUTHOR
Gary W. Adamson, Aug 27 2008
EXTENSIONS
More terms from Naohiro Nomoto, Aug 05 2012
STATUS
approved

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Last modified March 28 15:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)