A037276 Start with 1; for n>1, replace n with the concatenation of its prime factors in increasing order.

1, 2, 3, 22, 5, 23, 7, 222, 33, 25, 11, 223, 13, 27, 35, 2222, 17, 233, 19, 225, 37, 211, 23, 2223, 55, 213, 333, 227, 29, 235, 31, 22222, 311, 217, 57, 2233, 37, 219, 313, 2225, 41, 237, 43, 2211, 335, 223, 47, 22223, 77, 255, 317, 2213, 53, 2333

Offset

1,2

Links

N. J. A. Sloane, Table of n, a(n) for n = 1..20000 [First 10000 terms from T. D. Noe]

Patrick De Geest, Home Primes

N. J. A. Sloane, Confessions of a Sequence Addict (AofA2017), slides of invited talk given at AofA 2017, Jun 19 2017, Princeton. Mentions this sequence.

N. J. A. Sloane, Three (No, 8) Lovely Problems from the OEIS, Experimental Mathematics Seminar, Rutgers University, Oct 05 2017, Part I, Part 2, Slides. (Mentions this sequence)

Eric Weisstein's World of Mathematics, Home Prime

Example

If n = 2^3*5^5*11^2 = 3025000, a(n) = 222555551111 (n=2*2*2*5*5*5*5*5*11*11, then remove the multiplication signs).

Maple

# This is for n>1
read("transforms") ;
A037276 := proc(n)
    local L, p ;
    L := [] ;
    for p in ifactors(n)[2] do
        L := [op(L), seq(op(1, p), i=1..op(2, p))] ;
    end do:
    digcatL(L) ;
end proc: # R. J. Mathar, Oct 29 2012

Mathematica

co[n_, k_] := Nest[Flatten[IntegerDigits[{#, n}]] &, n, k - 1]; Table[FromDigits[Flatten[IntegerDigits[co @@@ FactorInteger[n]]]], {n, 54}] (* Jayanta Basu, Jul 04 2013 *)
FromDigits@ Flatten@ IntegerDigits[Table[#1, {#2}] & @@@ FactorInteger@ #] & /@ Range@ 54 (* Michael De Vlieger, Jul 14 2015 *)

Prog

(PARI) a(n)={ n<4 & return(n); for(i=1, #n=factor(n)~, n[1, i]=concat(vector(n[2, i], j, Str(n[1, i])))); eval(concat(n[1, ]))}  \\ M. F. Hasler, Jun 19 2011
(Haskell)
a037276 = read . concatMap show . a027746_row
-- Reinhard Zumkeller, Apr 03 2012
(Python)
from sympy import factorint
def a(n):
    f=factorint(n)
    l=sorted(f)
    return 1 if n==1 else int("".join(str(i)*f[i] for i in l))
print([a(n) for n in range(1, 101)]) # Indranil Ghosh, Jun 23 2017

Crossrefs

Cf. A037274, A048985, A067599, A080670, A084796. Different from A073646.

Cf. also A027746, A289660 (a(n)-n).

Sequence in context: A288532 A073647 A073646 * A068190 A084796 A084797

Adjacent sequences: A037273 A037274 A037275 * A037277 A037278 A037279

Keyword

nonn,easy,base

Author

N. J. A. Sloane

Status

approved