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%I #13 Sep 08 2022 08:46:26
%S 421,30661,50821,54421,130021,195541,423781,635461,1003381,1577941,
%T 1597381,1883941,2070421,2100661,2162581,2534821,2585941,2666581,
%U 2851621,3296581,3658021,3800581,4657381,4969141,5739541,5962741,6188821,6537301,6556741,7090261
%N Primes p such that p, p + 1, p + 2 and p + 3 have 2, 4, 6 and 8 divisors respectively.
%C Primes from A340157.
%C Term 1524085621 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. No such run exists for any 6 consecutive integers with prime p with this property (see A294528).
%e tau(421) = 2, tau (422) = 4, tau (423) = 6, tau (424) = 8.
%t Select[Range[10^6], DivisorSigma[0, # + {0, 1, 2, 3}] == {2, 4, 6, 8} &] (* _Amiram Eldar_, Jan 25 2021 *)
%t Select[Prime[Range[490000]],DivisorSigma[0,#+{1,2,3}]=={4,6,8}&] (* _Harvey P. Dale_, Oct 02 2021 *)
%o (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 Cf. A000005, A294528, A340157.
%K nonn
%O 1,1
%A _Jaroslav Krizek_, Jan 24 2021
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