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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
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
Sequence in context: A130703 A050939 A196547 * A036266 A087722 A217005
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.)