A106554 Concatenation of the two prime divisors of a semiprime, smallest divisor first.

22, 23, 33, 25, 27, 35, 37, 211, 55, 213, 311, 217, 57, 219, 313, 223, 77, 317, 511, 319, 229, 231, 513, 323, 237, 711, 241, 517, 243, 329, 713, 331, 247, 519, 253, 337, 523, 259, 717, 1111, 261, 341, 343, 719, 267, 347, 271, 1113

Offset: 1

Author

Eric Angelini, May 09 2005

Keywords

• base
• easy
• nonn

Comments

Concatenation of the divisors starting with the largest one leads to another sequence.

Examples

			First semiprime is 4; 4 is 2*2 -> 22.
Second semiprime is 6; 6 is 2*3 -> 23.
Third semiprime is 9; 9 is 3*3 -> 33.
Fourth semiprime is 10; 10 is 2*5 -> 25.
		

Links

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

Crossrefs

Cf. A106550, A084126, A084127, A001358.

Programs

Maple

read("transforms") :
A106554 := proc(n)
    A037276(A001358(n)) ;
end proc: # R. J. Mathar, Oct 29 2012

Mathematica

FromDigits@ Flatten[IntegerDigits@ Table[#1, {#2}] & @@@ FactorInteger@ #] & /@ Select[Range@ 144, PrimeOmega@ # == 2 &] (* Michael De Vlieger, Oct 01 2015 *)

PARI

do(x)=my(v=List()); forprime(p=2, sqrt(x), forprime(q=p, x\p, listput(v, [p*q, eval(Str(p, q))]))); Vec(apply(u->u[2], vecsort(v, 1))) \\ Charles R Greathouse IV, Sep 30 2015

Formula

a(n) = A037276(A001358(n)). - R. J. Mathar, Oct 29 2012

Extensions

More terms from Reinhard Zumkeller, May 19 2005

Data corrected by Giovanni Teofilatto and Altug Alkan, Oct 01 2015