A079093 -id:A079093 - cp's OEIS frontend

A079079 a(n) = (prime(n)+1)*(prime(n+1)+1)/4.

3, 6, 12, 24, 42, 63, 90, 120, 180, 240, 304, 399, 462, 528, 648, 810, 930, 1054, 1224, 1332, 1480, 1680, 1890, 2205, 2499, 2652, 2808, 2970, 3135, 3648, 4224, 4554, 4830, 5250, 5700, 6004, 6478, 6888, 7308, 7830, 8190, 8736, 9312, 9603, 9900, 10600

Offset: 1

Reinhard Zumkeller, Dec 22 2002

nonn

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A079080, A079081, A079082, A079095, smallest, greatest factor: A079083, A079084, number of factors: A079085, A079086, A079087, number, sum of divisors: A079088, A079089, sum of prime factors: A079090, A079091, Euler's totient: A079092, squarefree kernel: A079093, arithmetic derivative: A079094.

a079079 n = a079079_list !! (n-1)
a079079_list = map (`div` 4) $
               zipWith (*) a008864_list $ tail a008864_list
-- Reinhard Zumkeller, Oct 08 2012

Table[(Prime[n] + 1)*(Prime[n + 1] + 1)/4, {n, 1, 50}] (* G. C. Greubel, Apr 25 2017 *)

a(n)=(prime(n)+1)*(prime(n+1)+1)/4 \\ Charles R Greathouse IV, Aug 21 2011

from sympy import prime
def a(n): return (prime(n) + 1)*(prime(n + 1) + 1)/4 # Indranil Ghosh, Apr 26 2017

A079095 Squarefree numbers of the form (prime(k)+1)*(prime(k+1)+1)/4.

Original entry on oeis.org

3, 6, 42, 399, 462, 930, 1054, 3135, 4830, 6478, 13110, 19599, 20022, 24963, 26394, 35530, 38805, 39999, 41205, 44310, 52899, 71002, 74254, 81510, 94863, 95790, 103362, 109230, 111547, 114243, 135790, 144399, 146685, 157206, 166866, 183183

Offset: 1

Reinhard Zumkeller, Dec 22 2002

nonn

			(A000040(12)+1)*(A000040(12+1)+1)/4 = (37+1)*(41+1)/4 = 399 = 3*7*19, therefore 399 is a term.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Intersection of A005117 and A079079.

Cf. A000040, A008966, A079093.

a079095 n = a079095_list !! (n-1)
a079095_list = filter ((== 1) . a008966) a079079_list
-- Reinhard Zumkeller, Oct 09 2012

With[{p = Prime[Range[150]]}, Select[(Most[p]+1) * (Rest[p]+1) / 4, SquareFreeQ]] (* Amiram Eldar, Apr 06 2025 *)

A008966(a(n)) = 1.

A079094 Arithmetic derivative of (prime(n)+1)*(prime(n+1)+1)/4.

Original entry on oeis.org

1, 5, 16, 44, 41, 51, 123, 244, 336, 608, 624, 211, 493, 1280, 1836, 1647, 991, 623, 2724, 2256, 2556, 4496, 3483, 2541, 1694, 3896, 7236, 5319, 2122, 12352, 16576, 5925, 5891, 8275, 10180, 6396, 3479, 13780, 13476, 13581, 12993, 26672, 26480

Offset: 1

Reinhard Zumkeller, Dec 22 2002

nonn

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A003415, A079079, A079093.

a079094 = a003415 . a079079  -- Reinhard Zumkeller, Oct 09 2012

ad[n_] := n * Plus @@ ((Last[#]/First[#]) & /@ FactorInteger[n]); a[n_] := ad[(Prime[n]+1) * (Prime[n+1]+1) / 4]; Array[a, 100] (* Amiram Eldar, Apr 06 2025 *)

a(n) = A003415(A079079(n)).

cp's OEIS Frontend

A079079 a(n) = (prime(n)+1)*(prime(n+1)+1)/4.

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A079095 Squarefree numbers of the form (prime(k)+1)*(prime(k+1)+1)/4.

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A079094 Arithmetic derivative of (prime(n)+1)*(prime(n+1)+1)/4.

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