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

210, 330, 390, 462, 510, 546, 570, 690, 714, 770, 798, 858, 870, 910, 930, 966, 1110, 1122, 1190, 1218, 1230, 1254, 1290, 1302, 1326, 1330, 1410, 1430, 1482, 1518, 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

Offset

1,1

Comments

This sequence is not 2*{A046389}. 2618 = 2*1309 is not in this sequence, while 1309 is in A046389.

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

a(43) = 2002 is the only term coprime to 15. - Charles R Greathouse IV, Jan 13 2025

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Formula

a(n) == 2 (mod 4).

a(n) ~ (1/6)*n log n/log log n. - Charles R Greathouse IV, Jan 13 2025

Example

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.
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.

Maple

filter:= proc(n) local F, t;
   F:= ifactors(n)[2];
   F[.., 2] = [1, 1, 1, 1] and mul(t[1]+1, t = F) > 2*n
end proc:
select(filter, [seq(i, i=2..3000, 4)]); # Robert Israel, Jan 09 2025

Mathematica

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 *)

Prog

(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

Crossrefs

Intersection of A005101 and A046386.

Cf. A001065, A378717, A379917.

Sequence in context: A376861 A350373 A046386 * A229272 A046402 A258359

Adjacent sequences: A379759 A379760 A379761 * A379763 A379764 A379765

Keyword

nonn

Author

Massimo Kofler, Jan 09 2025

Status

approved