A122123
Product of the first n 5-almost primes (A014614).
Original entry on oeis.org
32, 1536, 110592, 8847360, 955514880, 107017666560, 12842119987200, 2080423437926400, 349511137571635200, 61513960212607795200, 11072512838269403136000, 2214502567653880627200000, 460616534072007170457600000, 111929817779497742421196800000
Offset: 1
a(10) = 32 * 48 * 72 * 80 * 108 * 112 * 120 * 162 * 168 * 176 = 2^33 * 3^12 * 5^2 * 7^2 * 11 which has 50 prime factors with multiplicity.
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Rest[FoldList[Times,1,Select[Range[200],PrimeOmega[#]==5&]]] (* Harvey P. Dale, Feb 07 2012 *)
A122609
Product of the first n 5-almost primes (A014614), divided by product of the first n primes, rounded down.
Original entry on oeis.org
16, 256, 3686, 42130, 413642, 3563691, 25155471, 214483497, 1566662070, 9508018081, 55207846924, 298420794188, 1513939638809, 8555519354201, 45872146324653, 228495219428460, 1045656088909905, 4662597642352366, 19485482684457652, 82333025427285855
Offset: 1
a(1) = floor(32/2) = floor 16 = 16.
a(2) = floor(1536/6) = floor(256) = 256.
a(3) = floor(110592/30) = floor(3686.4) = 3686.
a(4) = floor(8847360/210) = floor(42130.2857) = 42130.
a(5) = floor(955514880/2310) = floor(413642.805) = 413642.
a(6) = floor(107017666560/30030) = floor(3563691.86) = 3563691.
a(7) = floor(12842119987200/510510) floor(61152952320/2431) = floor(25155471.95) = 25155471.
a(8) = floor(2080423437926400/9699690) = floor(214483497.712) = 214483497.
a(9) = floor(349511137571635200/223092870) = floor(1566662070.247) = 1566662070.
a(10) = floor(61513960212607795200/6469693230) = floor(9508018081.501) = 9508018081.
Cf.
A001222,
A002110,
A008585,
A014613,
A008587,
A086046,
A086047,
A122093,
A112141,
A114426,
A014614.
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q = Select[Range[900], PrimeOmega[#] == 5 &]; m = 1; Table[ Floor[ m *= q[[i]] / Prime[i]], {i, Length@ q}] (* Giovanni Resta, Jun 13 2016 *)
A382831
a(n) is the n-th n-almost-prime that is a partial sum of the sequence of n-almost-primes.
Original entry on oeis.org
2, 10, 964, 1804, 7820, 48120, 830817, 4895208, 11308160, 162802560, 394129476, 3763612800, 19823090472, 1018716103620, 9744542956800, 3989325082624, 329306801920000, 2978224618328064, 11804664377696256, 128906665137012736
Offset: 1
The first three members of A086062 that are 3-almost-primes are 8 = 2^3, 20 = 2^2 * 5 = 8 + 12, and 964 = 2^2 * 241 = 8 + 12 + 18 + ... + 92, so a(3) = 964.
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f:= proc(n) uses priqueue;
local pq,t,s,x,p,i,count;
initialize(pq);
insert([-2^n,2$n],pq);
s:= 0; count:= 0:
do
t:= extract(pq);
x:= -t[1];
s:= s + x;
if numtheory:-bigomega(s) = n then count:= count+1; if count = n then return s fi fi;
p:= nextprime(t[-1]);
for i from n+1 to 2 by -1 while t[i] = t[-1] do
insert([t[1]*(p/t[-1])^(n+2-i), op(t[2..i-1]), p$(n+2-i)], pq)
od;
od
end proc:
map(f, [$1..20]);
Showing 1-3 of 3 results.
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