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A278568 Twice odd prime powers.

%I A278568 #9 Feb 03 2025 20:11:33
%S A278568 2,6,10,14,18,22,26,34,38,46,50,54,58,62,74,82,86,94,98,106,118,122,
%T A278568 134,142,146,158,162,166,178,194,202,206,214,218,226,242,250,254,262,
%U A278568 274,278,298,302,314,326,334,338,346,358,362,382,386,394,398,422,446,454,458,466,478
%N A278568 Twice odd prime powers.
%H A278568 L. J. Corwin, <a href="/A033948/a033948.pdf">Irreducible polynomials over the integers which factor mod p for every p</a>, Unpublished Bell Labs Memo, Sep 07 1967 [Annotated scanned copy]
%o A278568 (Python)
%o A278568 from sympy import primepi, integer_nthroot
%o A278568 def A278568(n):
%o A278568     def bisection(f,kmin=0,kmax=1):
%o A278568         while f(kmax) > kmax: kmax <<= 1
%o A278568         kmin = kmax >> 1
%o A278568         while kmax-kmin > 1:
%o A278568             kmid = kmax+kmin>>1
%o A278568             if f(kmid) <= kmid:
%o A278568                 kmax = kmid
%o A278568             else:
%o A278568                 kmin = kmid
%o A278568         return kmax
%o A278568     def f(x): return int(n+x-1-sum(primepi(integer_nthroot(x,k)[0])-1 for k in range(1,x.bit_length())))
%o A278568     return bisection(f,n,n)<<1 # _Chai Wah Wu_, Feb 03 2025
%Y A278568 Twice A061345.
%K A278568 nonn
%O A278568 1,1
%A A278568 _N. J. A. Sloane_, Nov 26 2016