A136141 -id:A136141 - cp's OEIS frontend

A382566 Decimal expansion of Sum_{p prime} 1/((p - 1)^3*(p + 1)).

3, 6, 7, 9, 2, 1, 6, 2, 4, 6, 0, 6, 3, 8, 0, 9, 9, 7, 5, 9, 7, 2, 6, 1, 3, 7, 6, 5, 0, 3, 2, 9, 1, 1, 7, 0, 5, 6, 0, 3, 5, 7, 4, 7, 2, 1, 6, 3, 3, 8, 3, 8, 2, 6, 0, 1, 8, 2, 6, 9, 0, 6, 1, 5, 1, 7, 3, 4, 9, 2, 6, 6, 3, 5, 2, 4, 0, 1, 5, 6, 9, 6, 4, 8, 2, 8, 6, 9, 7, 6, 3, 7, 4, 2, 6, 7, 9, 3, 4, 9, 2, 5, 2

Offset: 0

Artur Jasinski, Mar 31 2025

			0.36792162460638099759726137650329117056035747216338382601826906151734926635240156964828...

Index to constants which are prime zeta sums {0,3,1}.

Cf. A086242, A136141, A179119, A380840.

sumeulerrat(1/((p-1)^3*(p+1))) \\ Amiram Eldar, Apr 02 2025

Equals A136141/8 - A086242/4 + A380840/2 + A179119/8.

Equals Sum_{k>=2} (k-1)^2 * P(2*k) + (k-1)*k * P(2*k+1), where P is the prime zeta function. - Amiram Eldar, Apr 02 2025

A382571 Decimal expansion of Sum_{p prime} 1/((p - 1)*(p + 1)^2).

Original entry on oeis.org

1, 5, 3, 6, 0, 7, 9, 9, 6, 7, 5, 0, 2, 0, 2, 9, 3, 8, 7, 4, 3, 8, 9, 1, 3, 2, 6, 3, 1, 1, 9, 9, 6, 3, 0, 5, 2, 4, 7, 0, 6, 3, 3, 6, 2, 7, 9, 9, 9, 3, 3, 2, 2, 6, 6, 3, 8, 4, 6, 0, 5, 9, 1, 7, 8, 7, 8, 7, 3, 7, 2, 6, 2, 8, 8, 4, 0, 8, 2, 1, 2, 3, 7, 6, 1, 3, 4, 9, 7, 8, 9, 5, 2, 1, 9, 1, 2, 0, 8, 1, 4, 0

Offset: 0

Artur Jasinski, Mar 31 2025

			0.153607996750202938743891326311996305247063362799933226638460591787...

Index to constants which are prime zeta sums {0,1,2}.

Cf. A136141, A179119, A382554.

sumeulerrat(1/((p-1)*(p+1)^2)) \\ Amiram Eldar, Apr 02 2025

Equals A136141/4 + A179119/4 - A382554/2.

Equals Sum_{k>=2} (k-1) * (P(2*k-1) - P(2*k)), where P is the prime zeta function. - Amiram Eldar, Apr 02 2025

A382572 Decimal expansion of Sum_{p prime} 1/((p - 1)^3*p^2).

Original entry on oeis.org

2, 6, 4, 6, 2, 1, 6, 9, 5, 3, 6, 9, 6, 2, 9, 3, 5, 6, 1, 8, 5, 3, 3, 6, 5, 5, 9, 9, 7, 2, 8, 3, 0, 2, 5, 5, 9, 6, 8, 5, 5, 7, 4, 8, 0, 1, 8, 4, 1, 4, 3, 0, 6, 1, 0, 5, 4, 0, 4, 4, 7, 2, 3, 8, 8, 7, 0, 2, 4, 2, 2, 2, 2, 7, 5, 7, 2, 4, 2, 3, 9, 6, 6, 5, 2, 7, 5, 7, 1, 4, 6, 5, 4, 5, 7, 0, 3, 1, 4, 4, 6, 0

Offset: 0

Artur Jasinski, Mar 31 2025

			0.2646216953696293561853365599728302559685574801841430610540447238870242222757242396652...

Index to constants which are prime zeta sums {2,3,0}.

Cf. A136141, A085548, A086242, A380840.

sumeulerrat(1/((p-1)^3*p^2)) \\ Amiram Eldar, Apr 01 2025

Equals -A085548 + 3*A136141 - 2*A086242 + A380840.

Equals Sum_{k>=5} ((k-4)*(k-3)/2) * P(k), where P is the prime zeta function. - Amiram Eldar, Apr 01 2025

A382573 Decimal expansion of Sum_{p prime} 1/((p - 1)^3*(p + 1)^2).

Original entry on oeis.org

1, 1, 9, 4, 4, 1, 3, 4, 9, 3, 5, 4, 2, 8, 6, 7, 2, 0, 5, 4, 9, 9, 1, 3, 2, 5, 6, 5, 1, 0, 7, 5, 7, 6, 4, 6, 4, 6, 0, 9, 3, 2, 1, 2, 8, 9, 8, 2, 0, 8, 9, 0, 6, 8, 8, 5, 8, 9, 2, 8, 1, 7, 8, 4, 7, 6, 6, 8, 4, 3, 0, 0, 3, 1, 0, 7, 4, 2, 2, 6, 4, 8, 7, 4, 1, 5, 7, 6, 4, 9, 2, 6, 9, 1, 4, 3, 0, 0, 0, 2, 7, 2

Offset: 0

Artur Jasinski, Mar 31 2025

			0.119441349354286720549913256510757646460932...

Index to constants which are prime zeta sums {0,3,2}.

Cf. A086242, A136141, A179119, A380840, A382554.

sumeulerrat(1/((p-1)^3*(p+1)^2)) \\ Amiram Eldar, Apr 02 2025

Equals 3*A136141/16 - A086242/4 + A380840/4 + 3*A179119/16 - A382554/8.

Equals Sum_{k>=3} ((k-2)*(k-1)/2) * (P(2*k-1) + P(2*k)), where P is the prime zeta function. - Amiram Eldar, Apr 02 2025

A382580 Decimal expansion of Sum_{p prime} 1/((p - 1)*(p + 1)^3).

Original entry on oeis.org

0, 4, 6, 4, 4, 5, 8, 5, 0, 1, 3, 1, 5, 3, 3, 2, 8, 2, 9, 4, 8, 2, 4, 6, 3, 6, 3, 7, 4, 1, 9, 5, 2, 4, 9, 0, 2, 6, 3, 3, 6, 8, 3, 0, 9, 2, 1, 4, 1, 2, 0, 9, 9, 2, 0, 0, 9, 5, 7, 2, 6, 1, 1, 7, 4, 1, 3, 7, 9, 0, 9, 8, 6, 1, 4, 2, 0, 2, 4, 7, 8, 2, 7, 0, 9, 2, 8, 0, 1, 9, 5, 7, 4, 0, 0, 3, 1, 3, 6, 0, 8, 4, 3

Offset: 0

Artur Jasinski, Mar 31 2025

			0.046445850131533282948246363741952490263368309214120992009572611741379098614202478270928...

Index to constants which are prime zeta sums {0,1,3}.

Cf. A136141, A179119, A382554, A382555.

sumeulerrat(1/((p-1)*(p+1)^3)) \\ Amiram Eldar, Apr 02 2025

Equals A136141/8 + A179119/8 - A382554/4 - A382555/2.

Equals Sum_{k>=2} (k-1)^2 * P(2*k) - (k-1)*k * P(2*k+1), where P is the prime zeta function. - Amiram Eldar, Apr 02 2025

A382581 Decimal expansion of Sum_{p prime} 1/((p - 1)^2*(p + 1)^3).

Original entry on oeis.org

0, 4, 1, 2, 9, 6, 5, 3, 7, 8, 8, 3, 1, 3, 7, 1, 3, 6, 7, 7, 4, 5, 9, 4, 2, 4, 9, 8, 6, 9, 9, 1, 1, 6, 9, 3, 6, 8, 7, 5, 6, 2, 4, 5, 2, 4, 9, 2, 5, 4, 2, 3, 4, 8, 1, 4, 5, 4, 2, 0, 0, 4, 6, 4, 1, 1, 3, 0, 0, 7, 8, 3, 5, 5, 8, 3, 5, 7, 2, 8, 0, 8, 1, 4, 5, 2, 1, 8, 2, 9, 1, 3, 0, 9, 8, 9, 3, 9, 9, 1, 4

Offset: 0

Artur Jasinski, Mar 31 2025

			0.0412965378831371367745942498699116936875624524925423481454200464113007835583572808145218...

Index to constants which are prime zeta sums {0,2,3}.

Cf. A086242, A136141, A179119, A382554, A382555.

sumeulerrat(1/((p-1)^2*(p+1)^3)) \\ Amiram Eldar, Apr 02 2025

Equals -3*A136141/16 + A086242/8 - 3*A179119/16 + A382554/4 + A382555/4.

Equals Sum_{k>=3} ((k-2)*(k-1)/2) * (P(2*k-1) - P(2*k)), where P is the prime zeta function. - Amiram Eldar, Apr 02 2025

A382582 Decimal expansion of Sum_{p prime} 1/((p - 1)p^2(p + 1)).

Original entry on oeis.org

0, 9, 9, 4, 4, 5, 8, 7, 7, 6, 1, 5, 9, 3, 3, 6, 8, 5, 9, 3, 3, 1, 8, 7, 6, 5, 9, 1, 3, 9, 0, 9, 5, 6, 4, 3, 9, 5, 8, 2, 6, 9, 0, 3, 4, 5, 3, 8, 7, 3, 5, 8, 3, 0, 4, 9, 4, 1, 9, 8, 4, 0, 3, 7, 0, 8, 4, 0, 0, 5, 7, 0, 2, 7, 7, 1, 5, 9, 7, 9, 6, 6, 2, 8, 7, 9, 3, 4, 3, 8, 8, 1, 3, 3, 7, 1, 1, 0, 2, 5, 0

Offset: 0

Artur Jasinski, Mar 31 2025

			0.099445877615933685933187659139095643958269034538735830494198403708400570277159...

Index to constants which are prime zeta sums {2,1,1}.

Cf. A085548, A136141, A179119.

sumeulerrat(1/((p-1)*p^2*(p+1))) \\ Amiram Eldar, Apr 01 2025

Equals -A085548 + A136141/2 + A179119/2.

Equals Sum_{k>=2} P(2*k), where P is the prime zeta function. - Amiram Eldar, Apr 01 2025

A382583 Decimal expansion of Sum_{p prime} 1/((p - 1)p^3(p + 1)).

Original entry on oeis.org

0, 4, 6, 7, 0, 0, 7, 3, 2, 0, 9, 3, 3, 5, 2, 4, 0, 7, 0, 0, 1, 5, 2, 3, 1, 2, 1, 2, 1, 8, 8, 9, 2, 1, 1, 6, 5, 1, 1, 8, 2, 8, 8, 3, 6, 3, 7, 8, 4, 0, 8, 5, 0, 6, 1, 9, 1, 7, 1, 6, 7, 1, 6, 5, 9, 5, 5, 1, 1, 8, 4, 1, 3, 2, 0, 0, 3, 3, 1, 3, 9, 1, 2, 0, 4, 1, 3, 5, 7, 5, 1, 1, 8, 0, 7, 0, 2, 9, 7, 0, 5, 7

Offset: 0

Artur Jasinski, Mar 31 2025

			0.04670073209335240700152312121889211651182883637840850619171671659551184132...

Index to constants which are prime zeta sums {3,1,1}.

Cf. A085541, A136141, A179119.

sumeulerrat(1/((p-1)*p^3*(p+1))) \\ Amiram Eldar, Apr 01 2025

Equals -A085541 + A136141/2 - A179119/2.

Equals Sum_{k>=3} P(2*k-1), where P is the prime zeta function. - Amiram Eldar, Apr 01 2025

A382585 Decimal expansion of Sum_{p prime} 1/((p - 1)^2p^2(p + 1)).

Original entry on oeis.org

0, 9, 0, 7, 7, 6, 5, 9, 9, 5, 3, 7, 0, 8, 8, 4, 2, 2, 3, 8, 0, 9, 3, 6, 9, 5, 8, 2, 5, 1, 8, 5, 3, 5, 9, 9, 0, 7, 8, 5, 3, 9, 7, 9, 8, 3, 5, 5, 0, 5, 0, 9, 7, 6, 6, 6, 4, 6, 9, 8, 8, 6, 3, 9, 1, 0, 2, 9, 1, 0, 5, 6, 6, 2, 4, 9, 1, 9, 7, 6, 8, 7, 9, 1, 2, 3, 7, 1, 2, 0, 1, 5, 5, 7, 4, 1, 1, 1, 6, 7, 9, 5, 1, 4, 2

Offset: 0

Artur Jasinski, Mar 31 2025

			0.09077659953708842238093695825185359907853979835505...

Index to constants which are prime zeta sums {2,2,1}.

Cf. A085548, A086242, A136141, A179119.

sumeulerrat(1/((p-1)^2*p^2*(p+1))) \\ Amiram Eldar, Apr 01 2025

Equals A085548 - 5*A136141/4 + A086242/2 - A179119/4.

Equals Sum_{k>=3} (k-2) * (P(2*k-1) + P(2*k)), where P is the prime zeta function. - Amiram Eldar, Apr 01 2025

A382586 Decimal expansion of Sum_{p prime} 1/((p - 1)^2p^3(p + 1)).

Original entry on oeis.org

0, 4, 4, 0, 7, 5, 8, 6, 7, 4, 4, 3, 7, 3, 6, 0, 1, 5, 3, 7, 9, 4, 1, 3, 8, 3, 7, 0, 3, 2, 9, 6, 1, 4, 8, 2, 5, 6, 6, 7, 1, 0, 9, 6, 1, 9, 7, 6, 6, 4, 2, 4, 7, 0, 4, 7, 2, 9, 8, 2, 1, 4, 7, 3, 1, 4, 7, 7, 9, 2, 1, 5, 3, 0, 4, 8, 8, 6, 6, 2, 9, 6, 7, 0, 8, 2, 3, 5, 4, 5, 0, 3, 7, 6, 7, 0, 8, 1, 9, 7, 3, 8, 0, 5, 4

Offset: 0

Artur Jasinski, Mar 31 2025

			0.044075867443736015379413837032961482566710961976642...

Index to constants which are prime zeta sums {3,2,1}.

Cf. A085541, A085548, A086242, A136141, A179119.

sumeulerrat(1/((p-1)^2*p^3*(p+1))) \\ Amiram Eldar, Apr 01 2025

Equals A085548 + A085541 - 7*A136141/4 + A086242/2 + A179119/4.

Equals Sum_{k>=3} (k-2) * (P(2*k) + P(2*k+1)), where P is the prime zeta function. - Amiram Eldar, Apr 01 2025

cp's OEIS Frontend

A382566 Decimal expansion of Sum_{p prime} 1/((p - 1)^3*(p + 1)).

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A382571 Decimal expansion of Sum_{p prime} 1/((p - 1)*(p + 1)^2).

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A382572 Decimal expansion of Sum_{p prime} 1/((p - 1)^3*p^2).

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A382573 Decimal expansion of Sum_{p prime} 1/((p - 1)^3*(p + 1)^2).

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A382580 Decimal expansion of Sum_{p prime} 1/((p - 1)*(p + 1)^3).

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A382581 Decimal expansion of Sum_{p prime} 1/((p - 1)^2*(p + 1)^3).

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A382582 Decimal expansion of Sum_{p prime} 1/((p - 1)*p^2*(p + 1)).

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A382583 Decimal expansion of Sum_{p prime} 1/((p - 1)*p^3*(p + 1)).

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A382582 Decimal expansion of Sum_{p prime} 1/((p - 1)p^2(p + 1)).

A382583 Decimal expansion of Sum_{p prime} 1/((p - 1)p^3(p + 1)).

A382585 Decimal expansion of Sum_{p prime} 1/((p - 1)^2p^2(p + 1)).

A382586 Decimal expansion of Sum_{p prime} 1/((p - 1)^2p^3(p + 1)).