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A081950
Smallest triangular number k such that k-1 has exactly n (not necessarily distinct) prime factors.
1
3, 10, 21, 55, 253, 325, 1081, 4753, 8001, 18145, 226801, 293761, 7378561, 1181953, 33566721, 184291201, 471905281, 75479041, 924908545, 4831985665, 8590131201, 137438167041, 146163916801, 1051224625153, 309236465665, 19791199862785, 4947797606401, 969769321758721, 1367526255427585, 5066549731786753
OFFSET
1,1
EXAMPLE
a(4) = 2*3*3*3+1 = 55.
MAPLE
f:= proc(n) local pq, t, v, i, q;
uses priqueue;
initialize(pq);
insert([-2^n, 2$n], pq);
do
t:= extract(pq);
v:= -t[1];
if issqr(9+8*v) then return v+1 fi;
q:= nextprime(t[-1]);
for i from 1 to n while t[-i] = t[-1] do
insert([t[1]*(q/t[-1])^i, op(t[2..-i-1]), q$i], pq)
od;
od
end proc:
map(f, [$1..30]); # Robert Israel, Aug 13 2024
CROSSREFS
Cf. A081951.
Sequence in context: A008837 A176098 A355389 * A204340 A331017 A207646
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Apr 02 2003
EXTENSIONS
Extended and edited by Ryan Propper, Jun 21 2005
a(24)-a(26) from Donovan Johnson, Jan 31 2009
a(27)-a(30) from Robert Israel, Aug 13 2024
STATUS
approved