A048985 Working in base 2, replace n with the concatenation of its prime divisors in increasing order (write answer in base 10).

1, 2, 3, 10, 5, 11, 7, 42, 15, 21, 11, 43, 13, 23, 29, 170, 17, 47, 19, 85, 31, 43, 23, 171, 45, 45, 63, 87, 29, 93, 31, 682, 59, 81, 47, 175, 37, 83, 61, 341, 41, 95, 43, 171, 125, 87, 47, 683, 63, 173, 113, 173, 53, 191, 91, 343, 115, 93, 59, 349, 61, 95, 127, 2730

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• nice
• base
• look

Examples

			15 = 3*5 -> 11.101 -> 11101 = 29, so a(15) = 29.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Patrick De Geest, Home Primes

Crossrefs

Cf. A037276, A048986, A064841.

Cf. A193652, A029744 (record values and where they occur).

Cf. A027746.

Programs

Haskell

-- import Data.List (unfoldr)
a048985 = foldr (\d v -> 2 * v + d) 0 . concatMap
   (unfoldr (\x -> if x == 0 then Nothing else Just $ swap $ divMod x 2))
   . reverse . a027746_row
-- Reinhard Zumkeller, Jul 16 2012

Mathematica

f[n_] := FromDigits[ Flatten[ IntegerDigits[ Flatten[ Table[ #1, {#2}] & @@@ FactorInteger@n], 2]], 2]; Array[f, 64] (* Robert G. Wilson v, Jun 02 2010 *)

Python

from sympy import factorint
def a(n):
    if n == 1: return 1
    return int("".join(bin(p)[2:]*e for p, e in factorint(n).items()), 2)
print([a(n) for n in range(1, 65)]) # Michael S. Branicky, Oct 07 2022

Extensions

More terms from Sam Alexander (pink2001x(AT)hotmail.com) and Michel ten Voorde