login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Sum of all squarefree numbers with greatest prime factor prime(n).
9

%I #19 Jan 08 2025 12:26:30

%S 1,2,9,60,504,6336,89856,1645056,33094656,801239040,24246190080,

%T 777550233600,29697402470400,1250501433753600,55083063155097600,

%U 2649111037319577600,143390180403000115200,8619643674791667302400,534710099148093259776000,36412881178052121329664000

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

%H Robert Israel, <a href="/A339360/b339360.txt">Table of n, a(n) for n = 0..349</a>

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

%e The initial terms are:

%e 1 = 1,

%e 2 = 2,

%e 9 = 3 + 6,

%e 60 = 5 + 10 + 15 + 30.

%p f:= proc(n) local i;

%p `if`(n=0, 1, ithprime(n)) *mul(1+ithprime(i),i=1..n-1)

%p end proc:

%p map(f, [$0..20]); # _Robert Israel_, Dec 08 2020

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

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

%Y A048672 takes prime indices to binary indices in squarefree numbers.

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

%Y A072047 counts prime factors of squarefree numbers.

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

%Y A339195 has this as row sums.

%Y A002110 lists primorials.

%Y A005117 lists squarefree numbers.

%Y A006881 lists squarefree semiprimes.

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

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

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

%Y A319247 lists reversed prime indices of squarefree numbers.

%Y A329631 lists prime indices of squarefree numbers.

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

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

%K nonn,changed

%O 0,2

%A _Gus Wiseman_, Dec 04 2020

%E a(0)=1 prepended by _Alois P. Heinz_, Jan 08 2025