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A280050 a(n) = Sum_{k=2..n} k/lpf(k), where lpf(k) is the least prime dividing k (A020639). 0

%I

%S 0,1,2,4,5,8,9,13,16,21,22,28,29,36,41,49,50,59,60,70,77,88,89,101,

%T 106,119,128,142,143,158,159,175,186,203,210,228,229,248,261,281,282,

%U 303,304,326,341,364,365,389,396,421,438,464,465,492,503,531,550,579,580,610,611,642,663,695,708,741,742,776,799,834,835

%N a(n) = Sum_{k=2..n} k/lpf(k), where lpf(k) is the least prime dividing k (A020639).

%C Sum of the largest proper divisors of all positive integers <= n.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ProperDivisor.html">Proper Divisor</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LeastPrimeFactor.html">Least Prime Factor</a>

%F a(n) = Sum_{k=2..n} k/A020639(k).

%F a(n) + 1 = Sum_{k=1..n} A032742(k).

%F a(p^k) = a(p^k-1) + p^(k-1), for p is prime.

%e For n = 8 the divisors of the first eight positive integers are {1}, {1, 2}, {1, 3}, {1, 2, 4}, {1, 5}, {1, 2, 3, 6}, {1, 7}, {1, 2, 4, 8}, so a(8) = 1 + 1 + 2 + 1 + 3 + 1 + 4 = 13.

%t Table[Sum[k/FactorInteger[k][[1, 1]], {k, 2, n}], {n, 71}]

%Y Cf. A001065, A020639, A032742, A046669, A046670, A153485.

%K nonn,easy

%O 1,3

%A _Ilya Gutkovskiy_, Jan 02 2017

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Last modified May 28 21:37 EDT 2020. Contains 334690 sequences. (Running on oeis4.)