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 A230625 Concatenate prime factorization written in binary, convert back to decimal. 13
 1, 2, 3, 10, 5, 11, 7, 11, 14, 21, 11, 43, 13, 23, 29, 20, 17, 46, 19, 85, 31, 43, 23, 47, 22, 45, 15, 87, 29, 93, 31, 21, 59, 81, 47, 174, 37, 83, 61, 93, 41, 95, 43, 171, 117, 87, 47, 83, 30, 86, 113, 173, 53, 47, 91, 95, 115, 93, 59, 349, 61, 95, 119, 22 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS As in A080670 the prime factorization is written as p1^e1*...*pN^eN (except for exponents eK = 1 which are omitted), with all factors and exponents in binary (cf. A007088). Then "^" and "*" signs are dropped, all binary digits are concatenated, and the result is converted back to decimal (base 10). - M. F. Hasler, Jun 21 2017 The first nontrivial fixed point of this function is 255987. Smaller numbers such that a(a(n)) = n are 1007, 1269; 1503, 3751. See A230627 for further information. - M. F. Hasler, Jun 21 2017 255987 is the only nontrivial fixed point less than 10000000. - Benjamin Knight, May 16 2018 LINKS Chai Wah Wu, Table of n, a(n) for n = 1..10000 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) EXAMPLE 6 = 2*3 = (in binary) 10*11 -> 1011 = 11 in base 10, so a(6) = 11. 20 = 2^2*5 = (in binary) 10^10*101 -> 1010101 = 85 in base 10, so a(20) = 85. MAPLE # take ifsSorted from A080670 A230625 := proc(n) local Ldgs, p, eb, pb, b ; b := 2; 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(A230625(n), n=1..30) ; # R. J. Mathar, Aug 05 2017 MATHEMATICA Table[FromDigits[#, 2] &@ Flatten@ Map[IntegerDigits[#, 2] &, FactorInteger[n] /. {p_, 1} :> {p}], {n, 64}] (* Michael De Vlieger, Jun 23 2017 *) PROG (Python) import sympy [int(''.join([bin(y)[2:] for x in sorted(sympy.ntheory.factorint(n).items()) for y in x if y != 1]), 2) for n in range(2, 100)] # compute a(n) for n > 1 # Chai Wah Wu, Jul 15 2014 (PARI) a(n) = {if (n==1, return(1)); f = factor(n); s = []; for (i=1, #f~, s = concat(s, binary(f[i, 1])); if (f[i, 2] != 1, s = concat(s, binary(f[i, 2]))); ); subst(Pol(s), x, 2); } \\ Michel Marcus, Jul 15 2014 (PARI) A230625(n)=n>1||return(1); fold((x, y)->if(y>1, x<

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