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

1,1

Comments

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

Links

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

Example

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.

Maple

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

Mathematica

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

Crossrefs

Intersection of A046387 and 2*A376734.

Cf. A376380, A351382, A007304.

Sequence in context: A317285 A253032 A251486 * A268469 A250442 A183824

Adjacent sequences: A376926 A376927 A376928 * A376930 A376931 A376932

Keyword

nonn

Author

Massimo Kofler, Oct 11 2024

Status

approved