A180868 Numbers n such that n and n+1 are semiprime powers.

9, 14, 15, 21, 25, 33, 34, 35, 38, 57, 64, 81, 85, 86, 93, 94, 118, 121, 122, 133, 141, 142, 145, 158, 177, 201, 202, 205, 213, 214, 215, 216, 217, 218, 225, 253, 298, 301, 302, 326, 334, 361, 381, 393, 394, 445, 446, 453, 481, 484, 501

Offset

1,1

Comments

This is to semiprimes A001358 and powers of semiprimes A085155 as A006549 is to primes A000040 and powers of primes A000961.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Formula

{ n : {n,n+1} is subset of {A085155} } = { n : n = A001358(i)^j and n+1 = A001358(k)^m }.

Example

15 is in the sequence because 15 = (3*5)^1 and 15+1 = 16 = (2*2)^2 are both semiprime powers.

Maple

spp:= proc(n) option remember; local l;
        if n<2 or isprime(n) then false
        else l:= ifactors(n)[2];
             if nops(l)>2 then false
           elif nops(l)=2 then evalb(l[1][2]=l[2][2])
           else evalb(irem(l[1][2], 2)=0)
             fi
        fi
      end:
a:= proc(n) option remember; local k;
      for k from 1+ `if`(n=1, 8, a(n-1))
        while not spp(k) or not spp(k+1)
      do od; k
    end:
seq(a(n), n=1..80);  # Alois P. Heinz, Jan 22 2011

Mathematica

sppQ[n_] := With[{f = FactorInteger[n][[All, 2]]}, n==1 || Length[f]==1 && EvenQ[f[[1]]] || Length[f]==2 && f[[1]]==f[[2]]];
Select[Range[1000], sppQ[#] && sppQ[#+1]&] (* Jean-François Alcover, Nov 21 2020 *)

Crossrefs

Cf. A000961, A001358, A006549, A085155.

Sequence in context: A130703 A050939 A196547 * A036266 A087722 A217005

Adjacent sequences: A180865 A180866 A180867 * A180869 A180870 A180871

Keyword

nonn,easy

Author

Jonathan Vos Post, Jan 22 2011

Extensions

More terms and edited by Alois P. Heinz, Jan 22 2011

Status

approved