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

%I A339360 #19 Jan 08 2025 12:26:30
%S A339360 1,2,9,60,504,6336,89856,1645056,33094656,801239040,24246190080,
%T A339360 777550233600,29697402470400,1250501433753600,55083063155097600,
%U A339360 2649111037319577600,143390180403000115200,8619643674791667302400,534710099148093259776000,36412881178052121329664000
%N A339360 Sum of all squarefree numbers with greatest prime factor prime(n).
%H A339360 Robert Israel, <a href="/A339360/b339360.txt">Table of n, a(n) for n = 0..349</a>
%F A339360 For n >= 1, a(n) = A054640(n-1) * prime(n).
%e A339360 The initial terms are:
%e A339360    1 = 1,
%e A339360    2 = 2,
%e A339360    9 = 3 + 6,
%e A339360   60 = 5 + 10 + 15 + 30.
%p A339360 f:= proc(n) local i;
%p A339360   `if`(n=0, 1, ithprime(n)) *mul(1+ithprime(i),i=1..n-1)
%p A339360 end proc:
%p A339360 map(f, [$0..20]); # _Robert Israel_, Dec 08 2020
%t A339360 Table[Sum[Times@@Prime/@stn,{stn,Select[Subsets[Range[n]],MemberQ[#,n]&]}],{n,10}]
%Y A339360 A010036 takes prime indices here to binary indices, row sums of A209862.
%Y A339360 A048672 takes prime indices to binary indices in squarefree numbers.
%Y A339360 A054640 divides the n-th term by prime(n), row sums of A261144.
%Y A339360 A072047 counts prime factors of squarefree numbers.
%Y A339360 A339194 is the restriction to semiprimes, row sums of A339116.
%Y A339360 A339195 has this as row sums.
%Y A339360 A002110 lists primorials.
%Y A339360 A005117 lists squarefree numbers.
%Y A339360 A006881 lists squarefree semiprimes.
%Y A339360 A056239 is the sum of prime indices of n (Heinz weight).
%Y A339360 A246867 groups squarefree numbers by weight, with row sums A147655.
%Y A339360 A319246 is the sum of prime indices of the n-th squarefree number.
%Y A339360 A319247 lists reversed prime indices of squarefree numbers.
%Y A339360 A329631 lists prime indices of squarefree numbers.
%Y A339360 A338899/A270650/A270652 give the prime indices of squarefree semiprimes.
%Y A339360 Cf. A001221, A014466, A098350, A168472, A282935, A302590, A326878, A338901.
%K A339360 nonn
%O A339360 0,2
%A A339360 _Gus Wiseman_, Dec 04 2020
%E A339360 a(0)=1 prepended by _Alois P. Heinz_, Jan 08 2025