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A379762 Products of 4 distinct prime numbers (or tetraprimes) that are abundant.

%I A379762 #54 May 07 2025 12:02:08
%S A379762 210,330,390,462,510,546,570,690,714,770,798,858,870,910,930,966,1110,
%T A379762 1122,1190,1218,1230,1254,1290,1302,1326,1330,1410,1430,1482,1518,
%U A379762 1554,1590,1610,1722,1770,1794,1806,1830,1870,1914,1938,1974,2002,2010,2030,2046,2090,2130,2170,2190,2210,2226,2262,2346,2370,2418,2442,2470,2478,2490,2530,2562,2590,2622
%N A379762 Products of 4 distinct prime numbers (or tetraprimes) that are abundant.
%C A379762 This sequence is not 2*{A046389}. 2618  = 2*1309 is not in this sequence, while 1309 is in A046389.
%C A379762 Contains 6*p*q if p and q are distinct primes > 3. The first term not of this form is 770. - _Robert Israel_, Jan 09 2025
%C A379762 a(43) = 2002 is the only term coprime to 15. - _Charles R Greathouse IV_, Jan 13 2025
%H A379762 Charles R Greathouse IV, <a href="/A379762/b379762.txt">Table of n, a(n) for n = 1..10000</a>
%F A379762 a(n) == 2 (mod 4).
%F A379762 a(n) ~ (1/6)*n log n/log log n. - _Charles R Greathouse IV_, Jan 13 2025
%e A379762 210 is a term because 210=2*3*5*7 is the product of four distinct primes and it is smaller than the sum of its proper divisors 366.
%e A379762 1155 is not a term because 1155=3*5*7*11 is the product of four distinct primes and it is larger than the sum of its proper divisors 1149.
%p A379762 filter:= proc(n) local F,t;
%p A379762    F:= ifactors(n)[2];
%p A379762    F[..,2] = [1,1,1,1] and mul(t[1]+1, t = F) > 2*n
%p A379762 end proc:
%p A379762 select(filter, [seq(i,i=2..3000, 4)]); # _Robert Israel_, Jan 09 2025
%t A379762 q[n_] := Module[{f = FactorInteger[n]}, f[[;; , 2]] == {1, 1, 1, 1} && Times @@ (1 + 1/f[[;; , 1]]) > 2]; Select[Range[3000], q] (* _Amiram Eldar_, Jan 09 2025 *)
%o A379762 (PARI) list(lim)=my(v=List(select(k->k<=lim, [1430, 1870, 2002, 2090, 2210, 2470, 2530, 2990, 3190, 3230, 3410, 3770, 4030, 4070, 4510, 4730, 5170, 5830]))); forprime(p=5,sqrtint(lim\6), my(t=6*p); forprime(q=p+2,lim\t, listput(v,t*q))); forprime(p=11,lim\70,listput(v,70*p)); Set(v) \\ _Charles R Greathouse IV_, Jan 13 2025
%Y A379762 Intersection of A005101 and A046386.
%Y A379762 Cf. A001065, A378717, A379917.
%K A379762 nonn
%O A379762 1,1
%A A379762 _Massimo Kofler_, Jan 09 2025