A087712 - OEIS

A087712

a(1) = 1; if n = k-th prime, a(n) = k; otherwise write all prime factors of n in nondecreasing order, replace each prime with its rank, and concatenate the ranks.

1, 1, 2, 11, 3, 12, 4, 111, 22, 13, 5, 112, 6, 14, 23, 1111, 7, 122, 8, 113, 24, 15, 9, 1112, 33, 16, 222, 114, 10, 123, 11, 11111, 25, 17, 34, 1122, 12, 18, 26, 1113, 13, 124, 14, 115, 223, 19, 15, 11112, 44, 133, 27, 116, 16, 1222, 35, 1114, 28, 110, 17, 1123, 18

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OFFSET

1,3

COMMENTS

Concatenations of consecutive entries of A112798. - R. J. Mathar, Feb 09 2009

The old entry with this A-number was a duplicate of A082467.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

EXAMPLE

n = 2 = first prime, a(2) = 1.

n = 3 = second prime, a(3) = 2.

n = 4 = 2*2 -> 1,1 -> 11, so a(4) = 11.

n = 6 = 2*3 -> 1,2 -> 12, so a(6) = 12.

n = 12 = 2*2*3 -> 1,1,2 -> 112, so a(12) = 112.

MAPLE

# Maple program from R. J. Mathar, Feb 08 2009: (Start)

cat2 := proc(a, b) a*10^(max(1, ilog10(b)+1))+b ; end:

A049084 := proc(p) if isprime(p) then numtheory[pi](p) ; else 0 ; fi; end:

A087712 := proc(n) local pf, a, p, ex ; if isprime(n) then A049084(n) ; elif n = 1 then 1 ; else pf := ifactors(n)[2] ; a := 0 ; for p in pf do for ex from 1 to op(2, p) do a := cat2(a, A049084(op(1, p)) ) ; od: od: fi; end:

seq(A087712(n), n=1..140); # (End)

# (Maple program from David Applegate and N. J. A. Sloane, Feb 09 2009)

with(numtheory):

f := proc(n) local t1, v, r, x, j;

if (n = 1) then return 1; end if;

t1 := ifactors(n): v := 0;

for x in op(2, t1) do r := pi(x[1]):

for j from 1 to x[2] do

v := v * 10^length(r) + r;

end do; end do; v; end proc;

MATHEMATICA

f[n_] := If[n == 1, 1, FromDigits@ Flatten[ IntegerDigits@# & /@ (PrimePi@# & /@ Flatten[ Table[ First@#, {Last@#}] & /@ FactorInteger@ n])]]; Array[f, 61] (* Robert G. Wilson v, Jun 06 2011 *)

PROG

(Haskell)

a087712 1 = 1

a087712 n = read $ concatMap (show . a049084) $ a027746_row n :: Integer

-- Reinhard Zumkeller, Oct 03 2012

(Python)

from sympy import factorint, primepi

def a(n):

if n == 1: return 1

return int("".join(str(primepi(p))*e for p, e in factorint(n).items()))

print([a(n) for n in range(1, 62)]) # Michael S. Branicky, Oct 01 2024

CROSSREFS