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A340871 Primes p such that p, p + 1, p + 2 and p + 3 have 2, 4, 6 and 8 divisors respectively. 2
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 (list; graph; refs; listen; history; text; internal format)
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 *)

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

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Last modified September 24 09:10 EDT 2021. Contains 347630 sequences. (Running on oeis4.)