A048803 -id:A048803 - cp's OEIS frontend

A304066 a(n) = Sum_{k=1..n} k*floor(n/prime(k)).

0, 1, 3, 4, 7, 10, 14, 15, 17, 21, 26, 29, 35, 40, 45, 46, 53, 56, 64, 68, 74, 80, 89, 92, 95, 102, 104, 109, 119, 125, 136, 137, 144, 152, 159, 162, 174, 183, 191, 195, 208, 215, 229, 235, 240, 250, 265, 268, 272, 276, 285, 292, 308, 311, 319, 324, 334, 345, 362, 368, 386, 398, 404, 405, 414

Offset: 1

Ilya Gutkovskiy, May 05 2018

nonn

Partial sums of A066328.

Index entries for sequences computed from indices in prime factorization

Cf. A000040, A000720, A008472, A013939, A024916, A024924, A048803, A056239, A066328, A081401, A304038.

seq(add(k*floor(n/ithprime(k)),k=1..n),n=1..65); # Paolo P. Lava, May 14 2018

Table[Sum[k Floor[n/Prime[k]], {k, n}], {n, 65}]
nmax = 65; Rest[CoefficientList[Series[1/(1 - x) Sum[k x^Prime[k]/(1 - x^Prime[k]), {k, 1, nmax}], {x, 0, nmax}], x]]
a[n_] := Plus @@ (PrimePi[#[[1]]] & /@ FactorInteger[n]); a[1] = 0; Accumulate[Table[a[n], {n, 65}]]

G.f.: (1/(1 - x))*Sum_{k>=1} k*x^prime(k)/(1 - x^prime(k)).
a(p^k) = a(p^k-1) + pi(p), where p is a prime and pi() = A000720.
a(n) = A056239(A048803(n)).

A330043 Product of largest prime power factors of numbers <= n.

Original entry on oeis.org

1, 1, 2, 6, 24, 120, 360, 2520, 20160, 181440, 907200, 9979200, 39916800, 518918400, 3632428800, 18162144000, 290594304000, 4940103168000, 44460928512000, 844757641728000, 4223788208640000, 29566517460480000, 325231692065280000, 7480328917501440000, 59842631340011520000

Offset: 0

Ilya Gutkovskiy, Nov 28 2019

nonn

Partial products of A034699.

Cf. A000720, A000961, A001221, A034699, A048803, A104350, A210208, A246655, A284521.

a[n_] := Product[Max[#[[1]]^#[[2]] & /@ FactorInteger@k], {k, 1, n}]; Table[a[n], {n, 0, 24}]

A001221(a(n)) = A000720(n).

cp's OEIS Frontend

A304066 a(n) = Sum_{k=1..n} k*floor(n/prime(k)).

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