OFFSET
1,2
COMMENTS
All terms under 1 million except 1, 2^6, 3^6, 5^6 and 7^6 have 6 nontrivial divisors, with p^6 for p prime having 5 nontrivial divisors, and so it seems that each term in the sequence is the product of three distinct numbers. - Edited by Robert Israel, Feb 04 2025
The majority of the terms are the product of 3 primes, but there are also terms in the form p*q*p^2, p*p^2*q, or p*p^2*p^3.
The first consecutive integers that appear in the sequence are a(45)=874 and a(46)=875.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
Tom Gadron, Java Program
EXAMPLE
24 is a term because the nontrivial divisors of 24 are 2,3,4,6,8,12, and 24=2*3*4.
30 is a term because the nontrivial divisors of 30 are 2,3,5,6,10,15, and 30=2*3*5.
135 is a term because the nontrivial divisors of 135 are 3,5,9,15,27,45, and 135=3*5*9.
729 is a term because the nontrivial divisors of 729 are 3,9,27,81,243, and 729=3*9*27.
MAPLE
isA379872 := proc(n)
local d;
numtheory[divisors](n) minus {1, n} ;
d := sort(convert(%, set)) ;
mul( op(i, d), i=1..floor((nops(d)+1)/2)) ;
if % = n then
true;
else
false;
end if;
end proc:
A379872 := proc(n)
option remember ;
if n =1 then
1;
else
for a from procname(n-1)+1 do
if isA379872(a) then
return a;
end if;
end do:
end if;
end proc:
seq(A379872(n), n=1..60) ; # R. J. Mathar, Jan 29 2025
MATHEMATICA
q[k_] := Times @@ Select[Divisors[k], #^2 <= k &] == k; Select[Range[1200], q] (* Amiram Eldar, Jan 05 2025 *)
PROG
(Java) \\ See Gadron link.
(PARI) isok(k) = my(d=divisors(k)); d=setminus(d, Set([1, k])); vecprod(Vec(d, #d\2 + #d%2)) == k; \\ Michel Marcus, Jan 05 2025
CROSSREFS
KEYWORD
nonn
AUTHOR
Tom Gadron, Jan 04 2025
STATUS
approved