A340871 Primes p such that p, p + 1, p + 2 and p + 3 have 2, 4, 6 and 8 divisors respectively.

421, 30661, 50821, 54421, 130021, 195541, 423781, 635461, 1003381, 1577941, 1597381, 1883941, 2070421, 2100661, 2162581, 2534821, 2585941, 2666581, 2851621, 3296581, 3658021, 3800581, 4657381, 4969141, 5739541, 5962741, 6188821, 6537301, 6556741, 7090261

Offset

1,1

Comments

Primes from A340157.

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).

Links

Table of n, a(n) for n=1..30.

Example

tau(421) = 2, tau (422) = 4, tau (423) = 6, tau (424) = 8.

Mathematica

Select[Range[10^6], DivisorSigma[0, # + {0, 1, 2, 3}] == {2, 4, 6, 8} &] (* Amiram Eldar, Jan 25 2021 *)
Select[Prime[Range[490000]], DivisorSigma[0, #+{1, 2, 3}]=={4, 6, 8}&] (* Harvey P. Dale, Oct 02 2021 *)

Prog

(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]

Crossrefs

Cf. A000005, A294528, A340157.

Sequence in context: A303414 A242149 A083193 * A303334 A109505 A109473

Adjacent sequences: A340868 A340869 A340870 * A340872 A340873 A340874

Keyword

nonn

Author

Jaroslav Krizek, Jan 24 2021

Status

approved