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A068312 Arithmetic derivative of triangular numbers. 1
0, 1, 5, 7, 8, 10, 32, 60, 39, 16, 61, 71, 20, 71, 244, 212, 111, 123, 143, 247, 131, 34, 380, 520, 155, 378, 621, 275, 247, 263, 1008, 1280, 271, 239, 951, 795, 56, 343, 1256, 1004, 431, 451, 581, 1443, 942, 70, 2092, 2492, 840 (list; graph; refs; listen; history; internal format)
OFFSET

1,3

FORMULA

a(n) = A003415(A000217(n)).

EXAMPLE

a(7) = d(7*8/2) = d(28) = d(2*14) = d(2)*14 + 2*d(14) =

= 1*14 + 2*d(2*7) = 14 + 2*(2*d(7) + d(2)*7) =

= 14 + 2*(2*1 + 1*7) = 14 + 2*9 = 14 + 18 = 32;

where d(n) = A003415(n)

with d(1)=0, d(prime)=1 and d(m*n)=d(m)*n+m*d(n).

CROSSREFS

Sequence in context: A059612 A192270 A056657 * A082097 A088299 A013635

Adjacent sequences:  A068309 A068310 A068311 * A068313 A068314 A068315

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 25 2002

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Last modified February 17 19:13 EST 2012. Contains 206085 sequences.