A287637 a(n) = A249125(n)/concatenation of prime factors of A249125(n).

2, 4, 3, 8, 5, 9, 16, 7, 2, 32, 27, 4, 11, 25, 64, 13, 8, 81, 10, 128, 17, 49, 19, 16, 20, 256, 23, 125, 243, 32, 29, 31, 40, 512, 50, 121, 37, 64, 41, 43, 80, 1024, 729, 169, 47, 343, 100, 53, 625, 128, 59, 61, 160, 2048, 67, 289, 200, 71, 73, 79, 250, 256

Offset

1,1

Comments

The squares of the sequence are, in increasing order: 4, 9, 16, 25, 49, 64, 81, 100, 121, 169, 256, 289, 361, 400, 625, 729, 1024, 4096,... including the squares of the prime numbers.

The numbers p^n, p prime and n = 1, 2, 3, 4,... are in the sequence.

The twin primes (a(m), a(m+1)) of the sequence are (29, 31), (41, 43), (59, 61), (71, 73), (101, 103), (107, 109), (137, 139),...

The numbers whose prime factors are 2 and 5 (A033846) are in the sequence.

Links

Table of n, a(n) for n=1..62.

Example

a(9)=2 because A249125(9) = 50 and the concatenation of the prime factors of 50 is 25. Hence, 50/25 = 2.

Maple

with(numtheory):
for n from 2 to 10000 do:
  if type(n, prime)=false
   then
    x:=factorset(n):n0:=nops(x):
    d:=sum('length(x[i])', 'i'=1..n0):
    l:=sum('x[i]*10^sum('length(x[j])', 'j'=i+1..n0)', 'i'=1..n0):
    z:=n/l:
     if floor(z)=z
      then
      printf(`%d, `, z):
      else
     fi:
   fi:
od:

Mathematica

cf[n_] := FromDigits@ Flatten[ IntegerDigits /@ First /@ FactorInteger@n]; Reap[ Do[If[ CompositeQ[n] && IntegerQ[rz = n/cf[n]], Sow[rz]], {n, 6400}]][[2, 1]] (* Giovanni Resta, May 29 2017 *)

Crossrefs

Cf. A033846, A077800, A084317, A249125.

Sequence in context: A101905 A297075 A306458 * A053211 A131390 A131395

Adjacent sequences: A287634 A287635 A287636 * A287638 A287639 A287640

Keyword

nonn,base

Author

Michel Lagneau, May 28 2017

Status

approved