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A287637
a(n) = A249125(n)/concatenation of prime factors of A249125(n).
0
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.
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
KEYWORD
nonn,base
AUTHOR
Michel Lagneau, May 28 2017
STATUS
approved