A376380 -id:A376380 - cp's OEIS frontend

A378097 Products of 6 distinct primes that are sandwiched between twin prime numbers.

43890, 51870, 84630, 102102, 140070, 149730, 153510, 168630, 224070, 251790, 269178, 281190, 308490, 316470, 317730, 322770, 355110, 376530, 381990, 383838, 389298, 404430, 432390, 434010, 459030, 467670, 486330, 487830, 496230, 506730, 520410, 531570, 545790, 552090, 560490, 573342, 576030, 583338

Offset: 1

Massimo Kofler, Nov 16 2024

nonn

All the terms are divisible by 6.

			43890 is in the sequence a term because 43890=2*3*5*7*11*19 is the product of six distinct primes and 43889, 43891 are a couple of twin primes.
51870 is in the sequence a term because 51870=2*3*5*7*13*19 is the product of six distinct primes and 51869, 51871 are a couple of twin primes.

Intersection of A014574 and A067885.

Cf. A083207 (supersequence), A353022, A376380.

Select[6 * Range[10^5], PrimeQ[#-1] && PrimeQ[#+1] && FactorInteger[#][[;;, 2]] == {1,1,1,1,1,1} &] (* Amiram Eldar, Nov 16 2024 *)

A376929 Products of 5 distinct primes that are sandwiched between sphenic numbers.

Original entry on oeis.org

50610, 52206, 63546, 65190, 71890, 73830, 77406, 84930, 89310, 89870, 90390, 92598, 98210, 116754, 119210, 120990, 123410, 125994, 131054, 132430, 132870, 137410, 140998, 141702, 144430, 148190, 150306, 151810, 159942, 160854, 162470, 164406, 165110, 167314, 170562, 172938, 174306, 176946, 185658

Offset: 1

Massimo Kofler, Oct 11 2024

nonn

All terms are even.

Dickson's conjecture implies that there are infinitely many terms, e.g. there should be infinitely many k such that p = 241 + 104533*k, q = 229 + 99330*k, and r = 107 + 46410*k are all prime, and then 210*p is a term (with 210*p = 2*3*5*7*p, 210*p-1 = 13*17*q, and 210*p+1 = 11*43*r). - Robert Israel, Nov 12 2024

			50610 is a term because 50610=2*3*5*7*241 is the product of five distinct primes and 50609=13*17*229, 50611=11*43*107 are sphenic numbers.
52206 is a term because 52206=2*3*7*11*113 is the product of five distinct primes and 52205=5*53*197, 52207=17*37*83 are sphenic numbers.

Robert Israel, Table of n, a(n) for n = 1..10000

Intersection of A046387 and 2*A376734.

Cf. A376380, A351382, A007304.

filter:= proc(n) local F;
  F:= ifactors(n)[2];
  if F[..,2] <> [1$5] then return false fi;
  F:= ifactors(n-1)[2];
  if F[..,2] <> [1$3] then return false fi;
  F:= ifactors(n+1)[2];
  F[..,2] = [1$3]
end proc:
select(filter, [seq(i,i=2..2*10^5,4)]); # Robert Israel, Nov 12 2024

SequencePosition[Map[#[[;; , 2]] &, FactorInteger[Range[200000]]], {{1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1}}][[;; , 1]] + 1 (* Amiram Eldar, Oct 11 2024 *)

A376949 Products of 5 distinct primes that are sandwiched between squarefree semiprime numbers.

Original entry on oeis.org

5610, 6510, 6630, 7770, 9570, 10230, 12558, 13530, 14190, 14586, 14790, 15834, 16590, 16770, 17710, 19734, 20670, 21630, 22610, 22890, 23478, 23730, 24882, 25662, 26970, 28490, 28938, 29370, 31110, 31710, 33306, 33558, 33990, 34410, 34710, 35178, 35742, 36330, 37230, 37758, 38346, 39130, 40890

Offset: 1

Massimo Kofler, Oct 10 2024

nonn

All terms are even.

			5610 is a term because 5610=2*3*5*11*17 is the product of five distinct primes and 5609=71*79, 5611=31*181 are semiprime numbers.
6510 is a term because 6510=2*3*5*7*31 is the product of five distinct primes and 6509=23*283, 6511=17*383 are semiprime numbers.

Intersection of A046387 and 2*A350101.

Cf. A046387, A376380, A006881.

SequencePosition[Map[#[[;; , 2]] &, FactorInteger[Range[41000]]], {{1, 1}, {1, 1, 1, 1, 1}, {1, 1}}][[;; , 1]] + 1 (* Amiram Eldar, Oct 10 2024 *)

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A378097 Products of 6 distinct primes that are sandwiched between twin prime numbers.

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A376929 Products of 5 distinct primes that are sandwiched between sphenic numbers.

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A376949 Products of 5 distinct primes that are sandwiched between squarefree semiprime numbers.

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