A289667 Concatenate prime factorization written in base 3, convert back to decimal.

1, 2, 3, 8, 5, 21, 7, 21, 11, 23, 11, 75, 13, 25, 32, 22, 17, 65, 19, 77, 34, 65, 23, 192, 17, 67, 30, 79, 29, 194, 31, 23, 92, 71, 52, 227, 37, 73, 94, 194, 41, 196, 43, 227, 104, 77, 47, 201, 23, 71, 98, 229, 53, 192, 146, 196, 100, 191, 59, 680, 61, 193, 106, 24

Offset: 1

Author

N. J. A. Sloane, Jul 27 2017

Keywords

• nonn
• base

Comments

A080670 is the base 10 version, A230625 is the binary version.

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A080670, A195264, A230625, A230627.

Programs

Maple

# take ifsSorted from A080670
A289667 := proc(n)
    local Ldgs, p,eb,pb,b ;
    b := 3;
    if n = 1 then
        return 1;
    end if;
    Ldgs := [] ;
    for p in ifsSorted(n) do
        pb := convert(op(1,p),base,b) ;
        Ldgs := [op(pb),op(Ldgs)] ;
        if op(2, p) > 1 then
            eb := convert(op(2,p),base,b) ;
            Ldgs := [op(eb),op(Ldgs)] ;
        end if;
    end do:
    add( op(e,Ldgs)*b^(e-1),e=1..nops(Ldgs)) ;
end proc:
seq(A289667(n),n=1..30) ; # R. J. Mathar, Aug 05 2017

Mathematica

Table[FromDigits[#, 3] &@ Flatten@ Map[IntegerDigits[#, 3] &, FactorInteger[n] /. {p_, e_} /; p > 0 :> If[e == 1, p, {p, e}]], {n, 64}] (* Michael De Vlieger, Jul 29 2017 *)

PARI

a(n) = {if (n==1, return(1)); f = factor(n); s = []; for (i=1, #f~, s = concat(s, digits(f[i, 1], 3)); if (f[i, 2] != 1, s = concat(s, digits(f[i, 2], 3))););  fromdigits(s, 3);} \\ Michel Marcus, Jul 27 2017

Extensions

More terms from Michel Marcus, Jul 27 2017