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A340872 Primes p such that p, p - 1, p - 2 and p - 3 have 2, 4, 6 and 8 divisors respectively.

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%I A340872 #9 Sep 08 2022 08:46:26
%S A340872 1019,226379,645419,893099,967259,1744859,1880939,1996859,2238779,
%T A340872 2435339,2999099,3316619,3734219,4092059,4269899,4344779,4511099,
%U A340872 4681739,4692539,5857499,5993579,6476699,6744539,6848939,6855419,8160059,8608619,8755499,9254459
%N A340872 Primes p such that p, p - 1, p - 2 and p - 3 have 2, 4, 6 and 8 divisors respectively.
%C A340872 Term 55414379 of this sequence is the smallest prime p such that p, p - 1, p - 2, p - 3 and p - 4 have 2, 4, 6, 8 and 10 divisors respectively.
%e A340872 tau (1016) = 8, tau(1017) = 6, tau(1018) = 4, tau(1019) = 2.
%t A340872 Select[Range[10^6], DivisorSigma[0, # - {0, 1, 2, 3}] == {2, 4, 6, 8} &] (* _Amiram Eldar_, Jan 25 2021 *)
%t A340872 Select[Prime[Range[620000]],DivisorSigma[0,#-{0,1,2,3}]=={2,4,6,8}&] (* _Harvey P. Dale_, Nov 19 2021 *)
%o A340872 (Magma) [m: m in [1..10^7] | IsPrime(m) and #Divisors(m - 1) eq 4 and #Divisors(m - 2) eq 6 and #Divisors(m - 3) eq 8]
%Y A340872 Cf. A000005 (tau), A340871.
%K A340872 nonn
%O A340872 1,1
%A A340872 _Jaroslav Krizek_, Jan 24 2021