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%I #16 May 03 2023 17:10:14
%S 17,19,97,149,163,197,199,241,293,307,337,349,449,491,523,557,577,739,
%T 773,811,881,883,991,1013,1051,1061,1151,1171,1249,1277,1279,1423,
%U 1451,1459,1471,1493,1531,1549,1601,1637,1667,1693,1709,1733,1747,1861,1949
%N Primes p where neither the number of divisors of p+1 nor the number of divisors of p-1 is a power of 2.
%H Harvey P. Dale, <a href="/A165320/b165320.txt">Table of n, a(n) for n = 1..1000</a>
%p isA000079 := proc(n) RETURN( n=1 or numtheory[factorset](n) = {2}) ; end: isA165320 := proc(n) RETURN ( isprime(n) and not isA000079(numtheory[tau](n-1)) and not isA000079(numtheory[tau](n+1)) ) ; end: for n from 1 to 10000 do if isA165320(n) then printf("%d,",n) ; fi; od: # _R. J. Mathar_, Sep 18 2009
%t fQ[n_] := Union[ IntegerQ@# & /@ Log[2, DivisorSigma[0, {n - 1, n + 1}]]] == {False}; Select[ Prime@ Range@ 300, fQ@# &] (* _Robert G. Wilson v_, Sep 16 2009 *)
%t Select[Prime[Range[300]],NoneTrue[Log2[DivisorSigma[0,#+{1,-1}]],IntegerQ]&] (* _Harvey P. Dale_, May 03 2023 *)
%Y Cf. A165318, A165319.
%K nonn
%O 1,1
%A _Leroy Quet_, Sep 14 2009
%E More terms from _Robert G. Wilson v_ and _R. J. Mathar_, Sep 16 2009