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

1019, 226379, 645419, 893099, 967259, 1744859, 1880939, 1996859, 2238779, 2435339, 2999099, 3316619, 3734219, 4092059, 4269899, 4344779, 4511099, 4681739, 4692539, 5857499, 5993579, 6476699, 6744539, 6848939, 6855419, 8160059, 8608619, 8755499, 9254459

Offset: 1

Author

Jaroslav Krizek, Jan 24 2021

Keywords

• nonn

Comments

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.

Examples

			tau (1016) = 8, tau(1017) = 6, tau(1018) = 4, tau(1019) = 2.
		

Crossrefs

Cf. A000005 (tau), A340871.

Programs

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]

Mathematica

Select[Range[10^6], DivisorSigma[0, # - {0, 1, 2, 3}] == {2, 4, 6, 8} &] (* Amiram Eldar, Jan 25 2021 *)
Select[Prime[Range[620000]],DivisorSigma[0,#-{0,1,2,3}]=={2,4,6,8}&] (* Harvey P. Dale, Nov 19 2021 *)