A079089 -id:A079089 - 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

A079090 Sum of distinct prime factors of (prime(n)+1)*(prime(n+1)+1)/4.

Original entry on oeis.org

3, 5, 5, 5, 12, 10, 10, 10, 10, 10, 21, 29, 23, 16, 5, 10, 41, 50, 22, 42, 44, 17, 17, 15, 27, 35, 18, 21, 38, 24, 16, 39, 40, 17, 29, 100, 122, 53, 41, 39, 30, 25, 102, 111, 21, 60, 62, 31, 52, 44, 23, 21, 23, 55, 59, 21, 27, 158, 189, 123, 83, 23, 36, 175, 213, 141, 98, 47

Offset: 1

Reinhard Zumkeller, Dec 22 2002

nonn

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

Cf. A008472, A079079, A079085, A079089, A079091.

a079090 = a008472 . a079079  -- Reinhard Zumkeller, Oct 09 2012

Total[Transpose[FactorInteger[((#[[1]]+1)(#[[2]]+1))/4]][[1]]]&/@ Partition[Prime[Range[70]],2,1] (* Harvey P. Dale, Apr 24 2015 *)

a(n) = vecsum(factor((prime(n)+1)*(prime(n+1)+1)/4)[, 1]); \\ Amiram Eldar, Apr 07 2025

a(n) = A008472(A079079(n)).

A079091 Sum of all prime factors of (prime(n)+1)*(prime(n+1)+1)/4.

Original entry on oeis.org

3, 5, 7, 9, 12, 13, 13, 14, 15, 16, 27, 29, 23, 22, 18, 19, 41, 50, 29, 47, 48, 23, 23, 25, 34, 37, 28, 27, 38, 34, 28, 42, 40, 27, 36, 102, 122, 57, 46, 45, 33, 33, 110, 114, 31, 69, 70, 39, 52, 47, 33, 36, 37, 61, 64, 32, 37, 162, 189, 123, 90, 37, 40, 177, 213, 141, 111, 60

Offset: 1

Reinhard Zumkeller, Dec 22 2002

nonn

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

Cf. A001414, A079079, A079086, A079089, A079090.

a079091 = a001414 . a079079  -- Reinhard Zumkeller, Oct 09 2012

Total[Times@@@FactorInteger[#]]&/@(Times@@(#+1)/4&/@Partition[ Prime[Range[100]],2,1]) (* Harvey P. Dale, May 26 2011 *)

a(n) = my(f = factor((prime(n)+1)*(prime(n+1)+1)/4)); f[, 1]~ * f[, 2]; \\ Amiram Eldar, Apr 07 2025

a(n) = A001414(A079079(n)).

cp's OEIS Frontend

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

Views

Author

Keywords

Links

Crossrefs

Programs

Haskell

Mathematica

PARI

Python

A079090 Sum of distinct prime factors of (prime(n)+1)*(prime(n+1)+1)/4.

Views

Author

Keywords

Links

Crossrefs

Programs

Haskell

Mathematica

PARI

Formula

A079091 Sum of all prime factors of (prime(n)+1)*(prime(n+1)+1)/4.

Views

Author

Keywords

Links

Crossrefs

Programs

Haskell

Mathematica

PARI

Formula