A023589 -id:A023589 - cp's OEIS frontend

A072055 a(n) = 2*prime(n)+1.

5, 7, 11, 15, 23, 27, 35, 39, 47, 59, 63, 75, 83, 87, 95, 107, 119, 123, 135, 143, 147, 159, 167, 179, 195, 203, 207, 215, 219, 227, 255, 263, 275, 279, 299, 303, 315, 327, 335, 347, 359, 363, 383, 387, 395, 399, 423, 447, 455, 459, 467, 479

Offset: 1

Reinhard Zumkeller, Jun 11 2002

nonn

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
R. P. Boas & N. J. A. Sloane, Correspondence, 1974

Cf. A000040, A005385, A023589, A023590, A023591, A023592, A023593, A072059, A023595, A072060, A072056, A072057, A072058, A072192, A165286, A278230.
One less than A089241. After the initial term equal to A166496.
Row 4 of A286625, column 4 of A286623.

a072055 = (+ 1) . (* 2) . a000040  -- Reinhard Zumkeller, Oct 10 2013

2*Prime[Range[60]]+1  (* Harvey P. Dale, Mar 31 2011 *)

a(n) = A089241(n)-1.

A072059 Smallest prime p such that 2*p+1 has n distinct prime factors.

Original entry on oeis.org

2, 7, 97, 577, 7507, 217717, 5232727, 75172597, 1617423307, 59844662377, 2750790860317, 109455887488447, 4621264673452927, 218071376383127767, 10914293640945722527, 662082573402158125717, 41249727342503299116997

Offset: 1

Reinhard Zumkeller, Jun 11 2002

nonn

Note that for each n=1,...,8, the product of the smallest n-1 distinct prime factors of 2*a(n)+1 is p(n)#/2, where p(n)# is the primorial (A002110) of the n-th prime - and the n-th distinct prime factor >= p(n+1). - Rick L. Shepherd, Jul 06 2002

			a(4)=577=A000040(106): 2*577+1 = 1155 = 11*7*5*3, 4 distinct factors.

Cf. A001221, A023589, A072055, A072060.

for (n=1,8, p=1; until(isprime(p) && omega(2*p+1)==n, p++); print1(p,","))

More terms from Rick L. Shepherd, Jul 06 2002

More terms from Don Reble, Apr 15 2003

A023516 Number of distinct prime divisors of prime(n)*prime(n-1) - 1.

Original entry on oeis.org

0, 1, 2, 2, 2, 2, 3, 3, 2, 3, 2, 3, 2, 2, 3, 4, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 4, 3, 2, 4, 2, 3, 2, 4, 3, 3, 4, 3, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 4, 2, 3, 3, 4, 4, 4, 4, 4, 3, 4, 2, 3, 4, 2, 4, 4, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 4, 3, 2, 4

Offset: 1

Clark Kimberling

nonn

This is taking prime(0)=1 (see first comment in A023515). - Vincenzo Librandi, Apr 27 2019

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Cf. A023515, A023524, A023568, A023575, A023582, A023589.

[#PrimeDivisors(NthPrime(n)*(NthPrime(n-1))-1): n in [1..100]]; // Vincenzo Librandi, Apr 27 2019

0,seq(nops(numtheory:-factorset(ithprime(n)*ithprime(n-1)-1)),n=2..120); # Muniru A Asiru, Apr 29 2019

Prepend[Table[PrimeNu[Prime[n] Prime[n-1] - 1], {n, 2, 80}],0] (* Vincenzo Librandi, Apr 27 2019 *)

a(n) = if (n==1, 0, omega(prime(n)*prime(n-1) - 1)); \\ Michel Marcus, Apr 30 2019

a(n) = A001221(A023515(n)).

cp's OEIS Frontend

A072055 a(n) = 2*prime(n)+1.

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A072059 Smallest prime p such that 2*p+1 has n distinct prime factors.

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A023516 Number of distinct prime divisors of prime(n)*prime(n-1) - 1.

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Mathematica

PARI

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