A376734 -id:A376734 - cp's OEIS frontend

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

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 *)

cp's OEIS Frontend

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

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