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 A180868 Numbers n such that n and n+1 are semiprime powers. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified July 18 15:51 EDT 2024. Contains 374388 sequences. (Running on oeis4.)