A280011 Let d(1) < d(2) < ... < d(q) be the q distinct prime divisors of an integer m. The sequence lists the numbers m such that d(k) == d(k+2) mod d(k+1) for k = 1,2,...,q-2.

30, 60, 66, 70, 90, 102, 120, 132, 138, 140, 150, 170, 174, 180, 195, 198, 204, 240, 246, 264, 270, 276, 280, 282, 286, 300, 306, 318, 322, 340, 345, 348, 350, 354, 357, 360, 370, 390, 396, 408, 414, 426, 450, 470, 480, 490, 492, 498, 518, 522, 528, 534, 540

Offset

1,1

Comments

The subsequence for q = 3 begins with {30, 60, 66, 70, 90, 102, 120, ...}

The subsequence for q = 4 begins with {390, 690, 780, 1170, 1290, ...}

The subsequence for q = 5 begins with {12090, 24180, 32370, 36270, ...}

The subsequence for q = 6 begins with {1656330, 2405910, 3312660, ...}

The subsequence for q = 7 begins with {1412849490, 1989687570, ...}

Number of terms < 10^k: 0, 5, 103, 1001, 7861, 60088, 476156, 3920881, 33312469, ..., . Robert G. Wilson v, Jan 06 2017

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..1002

Example

390 is in the sequence because the prime factors are {2, 3, 5, 13} and we have 2 == 5 (mod 3) and 3 == 13 (mod 5).
1656330 is in the sequence because the prime factors are {2, 3, 5, 13, 31, 137} and we have 2 == 5 (mod 3), 3 == 13 (mod 5), 5 == 31 (mod 13) and 13 == 137 mod 31.

Maple

with(numtheory):nn:=1000:
for n from 2 to nn do:
lst2:={}:x:=factorset(n):n0:=nops(x):lst1:={}:
   for m from 1 to n0-2 do:
    lst1:=lst1 union {x[m]}:
     if x[m]=irem(x[m+2], x[m+1])
      then
       lst2:=lst2 union {x[m]}:
       else
     fi:
  od:
   if lst2=lst1 and lst2 <> {}
    then
    printf(`%d, `, n):
    else
  fi:
od:

Mathematica

fQ[n_] := If[ PrimeNu@ n > 2, Block[{d = First@# & /@ FactorInteger@ n}, Union[ Mod[d[[# + 2]], d[[# + 1]]] == d[[#]] & /@ Range[ Length@ d - 2]] == {True}], False]; Select[Range@550, fQ] (* Robert G. Wilson v, Jan 02 2017 *)

Crossrefs

Sequence in context: A040870 A356176 A343340 * A175785 A051488 A305613

Adjacent sequences: A280008 A280009 A280010 * A280012 A280013 A280014

Keyword

nonn

Author

Michel Lagneau, Jan 02 2017

Status

approved