A340393 Treat the prime factors of n in ascending order as digits of a number in base "greatest prime factor + 1" and convert this number back to a decimal number.

2, 3, 8, 5, 11, 7, 26, 15, 17, 11, 43, 13, 23, 23, 80, 17, 47, 19, 89, 31, 35, 23, 171, 35, 41, 63, 151, 29, 95, 31, 242, 47, 53, 47, 175, 37, 59, 55, 521, 41, 159, 43, 323, 131, 71, 47, 683, 63, 107, 71, 433, 53, 191, 71, 1175, 79, 89, 59, 527, 61, 95, 223, 728

Offset

2,1

Links

Alois P. Heinz, Table of n, a(n) for n = 2..20000

Formula

a(p) = p for prime p.

Example

Some examples for the calculation of a(n):
(For digits 10,11...36 the letters A,B...Z are used.)
    n -> prime factors     -> a(n)(base) -> a(n)(base 10)
    6 -> 2 * 3             ->   23 (4)   ->   11
   20 -> 2 * 2 * 5         ->  225 (6)   ->   89
   33 -> 3 * 11            ->   3B (12)  ->   47
   56 -> 2 * 2 * 2 * 7     -> 2227 (8)   -> 1175
   62 -> 2 * 31            ->   2U (32)  ->   95
   72 -> 2 * 2 * 2 * 3 * 3 ->22233 (4)   ->  687
  100 -> 2 * 2 * 5 * 5     -> 2255 (6)   ->  539
  910 -> 2 * 5 * 7 * 13    -> 257D (14)  -> 6579

Maple

a:= n-> (l-> (m-> add(l[-i]*m^(i-1), i=1..nops(l)))(1+
    max(l)))(map(i-> i[1]$i[2], sort(ifactors(n)[2]))):
seq(a(n), n=2..77);  # Alois P. Heinz, Jan 09 2021

Prog

(Python)
def A(startn, lastn=0):
    a, n, lastn=[], startn, max(lastn, startn)
    while n<=lastn:
        i, j, v, m, f=2, 0, 0, n, []
        while i<m**(0.5)+0.1:
            if m//i==m/i:
                f.append(i)
                m, i=m//i, 1
            i+=1
        f.append(m)
        while j<len(f):v, j=v+f[j]*((f[len(f)-1]+1)**(len(f)-j-1)), j+1
        print(str(n)+" "+str(v))
        a.append([v])
        n+=1
    return a
(Python)
from sympy import factorint
def fromdigits(d, b):
  n = 0
  for di in d: n *= b; n += di
  return n
def a(n):
  f = sorted(factorint(n, multiple=True))
  return fromdigits(f, f[-1]+1)
print([a(n) for n in range(2, 76)]) # Michael S. Branicky, Jan 06 2021
(PARI) a(n) = my(f=factor(n), list=List()); for (k=1, #f~, for (j=1, f[k, 2], listput(list, f[k, 1]))); fromdigits(Vec(list), vecmax(f[, 1])+1); \\ Michel Marcus, Jan 06 2021

Crossrefs

Cf. A037274 (home primes), A037276, A340394.

Sequence in context: A011433 A349824 A332221 * A332222 A126139 A296070

Adjacent sequences: A340390 A340391 A340392 * A340394 A340395 A340396

Keyword

nonn,look,base

Author

S. Brunner, Jan 06 2021

Status

approved