A325198 Positive numbers whose maximum prime index minus minimum prime index is 2.

10, 20, 21, 30, 40, 50, 55, 60, 63, 80, 90, 91, 100, 105, 120, 147, 150, 160, 180, 187, 189, 200, 240, 247, 250, 270, 275, 300, 315, 320, 360, 385, 391, 400, 441, 450, 480, 500, 525, 540, 551, 567, 600, 605, 637, 640, 713, 720, 735, 750, 800, 810, 900, 945

Offset

1,1

Comments

Also Heinz numbers of integer partitions whose maximum minus minimum part is 2 (counted by A008805). The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

Links

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

Example

The sequence of terms together with their prime indices begins:
   10: {1,3}
   20: {1,1,3}
   21: {2,4}
   30: {1,2,3}
   40: {1,1,1,3}
   50: {1,3,3}
   55: {3,5}
   60: {1,1,2,3}
   63: {2,2,4}
   80: {1,1,1,1,3}
   90: {1,2,2,3}
   91: {4,6}
  100: {1,1,3,3}
  105: {2,3,4}
  120: {1,1,1,2,3}
  147: {2,4,4}
  150: {1,2,3,3}
  160: {1,1,1,1,1,3}
  180: {1,1,2,2,3}
  187: {5,7}

Maple

N:= 1000: # for terms <= N
q:= 2: r:= 3:
Res:= NULL:
do
  p:= q; q:= r; r:= nextprime(r);
  if p*r > N then break fi;
  for i from 1 do
    pi:= p^i;
    if pi*r > N then break fi;
    for j from 0 do
      piqj:= pi*q^j;
      if piqj*r > N then break fi;
      Res:= Res, seq(piqj*r^k, k=1 .. floor(log[r](N/piqj)))
    od
  od
od:
sort([Res]); # Robert Israel, Apr 12 2019

Mathematica

Select[Range[100], PrimePi[FactorInteger[#][[-1, 1]]]-PrimePi[FactorInteger[#][[1, 1]]]==2&]

Crossrefs

Positions of 2's in A243055.

A061395(a(n)) - A055396((n)) = 2.

Cf. A000961, A008805, A046660, A056239, A093641, A112798, A118914, A174090, A195086, A256617, A325180, A325197.

Sequence in context: A210589 A296714 A297147 * A098165 A104801 A364325

Adjacent sequences: A325195 A325196 A325197 * A325199 A325200 A325201

Keyword

nonn

Author

Gus Wiseman, Apr 11 2019

Status

approved