A339360 Sum of all squarefree numbers with greatest prime factor prime(n).

2, 9, 60, 504, 6336, 89856, 1645056, 33094656, 801239040, 24246190080, 777550233600, 29697402470400, 1250501433753600, 55083063155097600, 2649111037319577600, 143390180403000115200, 8619643674791667302400, 534710099148093259776000, 36412881178052121329664000

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..349

Formula

For n > 1, a(n) = A054640(n-1) * prime(n).

Example

The initial terms are:
   2 = 2
   9 = 3 + 6
  60 = 5 + 10 + 15 + 30

Maple

f:= proc(n) local i;
  ithprime(n) *mul(1+ithprime(i), i=1..n-1)
end proc:
map(f, [$1..20]); # Robert Israel, Dec 08 2020

Mathematica

Table[Sum[Times@@Prime/@stn, {stn, Select[Subsets[Range[n]], MemberQ[#, n]&]}], {n, 10}]

Crossrefs

A010036 takes prime indices here to binary indices, row sums of A209862.

A048672 takes prime indices to binary indices in squarefree numbers.

A054640 divides the n-th term by prime(n), row sums of A261144.

A072047 counts prime factors of squarefree numbers.

A339194 is the restriction to semiprimes, row sums of A339116.

A339195 has this as row sums.

A002110 lists primorials.

A005117 lists squarefree numbers.

A006881 lists squarefree semiprimes.

A056239 is the sum of prime indices of n (Heinz weight).

A246867 groups squarefree numbers by weight, with row sums A147655.

A319246 is the sum of prime indices of the n-th squarefree number.

A319247 lists reversed prime indices of squarefree numbers.

A329631 lists prime indices of squarefree numbers.

A338899/A270650/A270652 give the prime indices of squarefree semiprimes.

Cf. A001221, A014466, A098350, A168472, A282935, A302590, A326878, A338901.

Sequence in context: A354496 A357683 A120970 * A111558 A322943 A168449

Adjacent sequences: A339357 A339358 A339359 * A339361 A339362 A339363

Keyword

nonn

Author

Gus Wiseman, Dec 04 2020

Status

approved