A378717 Products of 4 distinct primes numbers (or tetraprimes) that are deficient.

1155, 1365, 1785, 1995, 2145, 2415, 2618, 2805, 2926, 3003, 3045, 3094, 3135, 3255, 3315, 3458, 3542, 3705, 3795, 3885, 3910, 3927, 4186, 4305, 4370, 4389, 4466, 4485, 4515, 4522, 4641, 4774, 4785, 4810, 4845, 4862, 4930, 4935, 5005, 5115, 5187, 5270, 5278, 5313, 5330, 5434, 5474, 5510, 5565, 5590

Offset

1,1

Links

Table of n, a(n) for n=1..50.

Formula

a(n) ~ A046390(n) ~ A046386(n) ~ A014613(n) ~ 6n log n / (log log n)^3. - Charles R Greathouse IV, Dec 06 2024

Example

1155 is 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 (1+3+5+7+11+15+21+33+35+55+77+105+165+231+385=1149).
1365 is a term because 1365=3*5*7*13 is the product of four distinct primes and it is larger than the sum of its proper divisors (1+3+5+7+13+15+21+35+39+65+91+105+195+273+455=1323).

Mathematica

q[n_] := Module[{f = FactorInteger[n]}, f[[;; , 2]] == {1, 1, 1, 1} && Times @@ (1 + 1/f[[;; , 1]]) < 2]; Select[Range[6000], q] (* Amiram Eldar, Dec 05 2024 *)

Prog

(PARI) catpr(~v, lim, mult, startAt)=forprime(p=startAt, lim\mult, listput(v, mult*p))
list(lim)=my(v=List()); forprime(p=3, sqrtnint(lim\=1, 4), forprime(q=p+2, sqrtnint(lim\p, 3), forprime(r=q+2, sqrtint(lim\p\q), catpr(~v, lim, p*q*r, r+2)))); forprime(p=11, sqrtnint(lim\2, 3), forprime(q=13, sqrtint(lim\2\p), catpr(~v, lim, 2*p*q, q+2))); forprime(p=13, sqrtint(lim\14), catpr(~v, lim, 14*p, p+2)); forprime(p=19, sqrtint(lim\10), catpr(~v, lim, 10*p, p+2)); catpr(~v, lim, 154, 17); catpr(~v, lim, 110, 59); catpr(~v, lim, 130, 37); catpr(~v, lim, 170, 23); Set(v) \\ Charles R Greathouse IV, Dec 06 2024

Crossrefs

Intersection of A005100 and A046386. A046390 is a subsequence.

Cf. A378480.

Sequence in context: A020382 A185689 A309413 * A046390 A234498 A147577

Adjacent sequences: A378714 A378715 A378716 * A378720 A378721 A378722

Keyword

nonn,new

Author

Massimo Kofler, Dec 05 2024

Status

approved