A143268 a(n) = phi(n)*T(n), where phi(n) is Euler's totient function (A000010) and T(n) = n*(n+1)/2 is the n-th triangular number (A000217).
1, 3, 12, 20, 60, 42, 168, 144, 270, 220, 660, 312, 1092, 630, 960, 1088, 2448, 1026, 3420, 1680, 2772, 2530, 6072, 2400, 6500, 4212, 6804, 4872, 12180, 3720, 14880, 8448, 11220, 9520, 15120, 7992, 25308, 13338, 18720, 13120, 34440, 10836, 39732
Offset: 1
Keywords
Examples
a(4) = 20 = phi(4) * T(4) = 2 * 10. a(4) = 20 = sum of row 4 terms of triangle A143267: (2 + 4 + 6 + 8).
Programs
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Maple
with(numtheory): seq((1/2)*n*(n+1)*phi(n),n=1..45); # Emeric Deutsch, Aug 23 2008
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PARI
a(n)=eulerphi(n)*n*(n+1)/2 \\ Charles R Greathouse IV, Mar 05 2013
Formula
a(n) = sum of n-th row of triangle A143267.
a(n) = n*(n+1)*phi(n)/2. - Emeric Deutsch, Aug 23 2008
Sum_{k=1..n} a(k) ~ c * n^4, where c = 3/(4*Pi^2) = A323669 / 10 = 0.0759908... . - Amiram Eldar, Nov 27 2024
Extensions
Extended by Emeric Deutsch, Aug 16 2008