A379917 -id:A379917 - cp's OEIS frontend

A379915 a(n) is the deficiency of the odd squarefree semiprime A046388(n), divided by 2.

3, 5, 9, 11, 11, 15, 19, 17, 23, 21, 29, 31, 27, 35, 29, 35, 35, 43, 47, 39, 41, 53, 45, 59, 55, 59, 51, 65, 57, 59, 71, 79, 65, 83, 79, 89, 69, 83, 89, 71, 95, 91, 77, 107, 81, 109, 107, 103, 87, 119, 95, 115, 131, 125, 99, 119, 101, 139, 105, 143, 107, 137, 131

Offset: 1

Hugo Pfoertner, Jan 06 2025

nonn

Hugo Pfoertner, Table of n, a(n) for n = 1..10000

Cf. A000203, A033879, A046388, A379916, A379917.

\\ uses function a379915_17 from A379917
a379915_17(300,2)

a(n) = (2*A046388(n) - sigma(A046388(n)))/2, where sigma is A000203.

a(n) = A033879(A046388(n))/2.

A379916 a(n) is the deficiency of A046389(n), divided by 2.

Original entry on oeis.org

9, 21, 27, 39, 39, 49, 45, 57, 69, 97, 79, 93, 75, 119, 81, 99, 99, 129, 163, 129, 111, 147, 117, 139, 159, 185, 129, 211, 181, 183, 169, 147, 229, 189, 165, 225, 199, 171, 287, 237, 249, 219, 329, 189, 295, 255, 325, 201, 317, 207, 349, 249, 291, 309, 225, 313

Offset: 1

Hugo Pfoertner, Jan 06 2025

nonn

Hugo Pfoertner, Table of n, a(n) for n = 1..10000

Cf. A000203, A033879, A046389, A379915, A379917.

\\ uses function a379915_17 from A379917
a379915_17(1210,3)

a(n) = (2*A046389(n) - sigma(A046389(n)))/2, where sigma is A000203.

a(n) = A033879(A046389(n))/2.

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

Original entry on oeis.org

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

Massimo Kofler, Jan 09 2025

nonn

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

			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.

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

Intersection of A005101 and A046386.

Cf. A001065, A378717, A379917.

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

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 *)

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

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

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

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A379915 a(n) is the deficiency of the odd squarefree semiprime A046388(n), divided by 2.

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A379916 a(n) is the deficiency of A046389(n), divided by 2.

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PARI

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

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