A122137 -id:A122137 - cp's OEIS frontend

A122136 Numerator of Sum[ Prime[k]^2, {k,1,n}] / Product[ Prime[k], {k,1,n}] = Numerator[ A024450[n] / A002110[n] ].

2, 13, 19, 29, 104, 29, 111, 79, 778, 47, 73, 163, 1068, 359, 5233, 885, 142, 20477, 219, 811, 2524, 13859, 2203, 56387, 10966, 75997, 3331, 6537, 54968, 1, 23139, 4457, 87382, 681, 15449, 239087, 108, 58061, 159097, 116041, 1882, 995, 74901, 7487

Offset: 1

Alexander Adamchuk, Aug 21 2006

a(n) = 1 for n = {30,123,195,214,248,300,304,335,343,350,364,367,414,443,543,570,579,584,590,612,671,691,...} = A122137. a(n) is prime for n = {1,2,3,4,6,8,10,11,12,14,15,18,20,22,23,26,27,32,36,...} = A122138. Prime a(n) are listed in A122139 = {2,13,19,29,29,79,47,73,163,359,5233,20477,811,13859,2203,75997,3331,...}.

Cf. A122137, A122138, A122139.

Table[Numerator[Sum[Prime[k]^2,{k,1,n}]/Product[Prime[k],{k,1,n}]],{n,1,100}]

a(n) = Numerator[ Sum[ Prime[k]^2, {k,1,n}] / Product[ Prime[k], {k,1,n}] ].

A122138 Indices k such that A122136(k) is a prime.

Original entry on oeis.org

1, 2, 3, 4, 6, 8, 10, 11, 12, 14, 15, 18, 20, 22, 23, 26, 27, 32, 36, 38, 39, 40, 44, 47, 48, 50, 51, 52, 54, 55, 56, 58, 59, 60, 64, 66, 68, 71, 72, 74, 76, 78, 80, 83, 84, 86, 88, 89, 90, 92, 94, 95, 96, 98, 100, 102, 103, 107, 108, 110, 112, 114, 116, 118, 120, 122, 126

Offset: 1

Alexander Adamchuk, Aug 21 2006

nonn

The corresponding primes are listed in A122139.

Cf. A122136, A122137, A122139, A002110, A024450, A007504, A098999, A122102, A122103.

Select[Range[200],PrimeQ[Numerator[Sum[Prime[k]^2,{k,1,#1}]/Product[Prime[k],{k,1,#1}]]]&]

A264897 Integers n such that A002110(n) is divisible by A098999(n).

Original entry on oeis.org

138, 163, 873, 1054, 1079, 1604, 1825, 1990, 2079, 2493, 2509, 2810, 2950, 3494, 3800, 3910, 4300, 4462, 4470, 4564, 4593, 4957, 5140, 5450, 5558, 5572, 5581, 5834, 6391, 6792, 6969, 7444, 7892, 8321, 8530, 8581, 9254, 9299, 9522, 9832, 9847, 10082, 10850

Offset: 1

Altug Alkan, Nov 27 2015

nonn

A002110(138) has 327 digits.

What is the minimum value of a(n) - a(n-1)?

Cf. A002110, A051838, A098999, A122137.

Select[Range@ 10000, Divisible[Product[Prime@ k, {k, #}], Sum[Prime[k]^3, {k, #}]] &] (* Michael De Vlieger, Nov 28 2015 *)

for(n=1, 11000, if(prod(k=1, n, prime(k)) % sum(k=1, n, prime(k)^3) == 0, print1(n, ", ")))

cp's OEIS Frontend

A122136 Numerator of Sum[ Prime[k]^2, {k,1,n}] / Product[ Prime[k], {k,1,n}] = Numerator[ A024450[n] / A002110[n] ].

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

Formula

A122138 Indices k such that A122136(k) is a prime.

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

A264897 Integers n such that A002110(n) is divisible by A098999(n).

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

PARI