A069459 -id:A069459 - cp's OEIS frontend

A069460 Greatest prime factor of prime(n)^n - 1.

2, 31, 5, 3221, 157, 25646167, 3833, 7792003, 732541, 150332843, 144061, 17615988547, 6177695707, 461017351, 31129845205681, 361353204962363828785531, 903870199, 751410597400064602523400427092397, 25058741, 153436090543, 1750258119644519

Offset: 2

Reinhard Zumkeller, Mar 24 2002

nonn

			A000040(9)^9 - 1 = 23^9 - 1 = 1801152661462 = 2*7*11*19*79*7792003, therefore a(9) = 7792003.

Hugo Pfoertner and Amiram Eldar, Table of n, a(n) for n = 2..96 (terms 2..50 from Hugo Pfoertner)
Dario Alpern, Factorization using the Elliptic Curve Method.
FactorDB, Status of 509^97-1.

Cf. A006530, A069459, A069463.

Table[FactorInteger[Prime[n]^n-1][[-1,1]],{n,2,30}] (* Harvey P. Dale, May 19 2019 *)

a(n) = A006530(A069459(n)).

More terms from Hugo Pfoertner, May 18 2004

Undefined a(1) removed by Hugo Pfoertner, Jul 22 2019

A069461 Number of distinct prime factors of prime(n)^n-1.

Original entry on oeis.org

0, 1, 2, 3, 3, 5, 2, 6, 6, 8, 7, 11, 5, 7, 9, 8, 5, 12, 4, 13, 8, 10, 4, 16, 7, 12, 12, 13, 6, 18, 4, 15, 10, 8, 10, 19, 8, 9, 8, 17, 5, 21, 5, 13, 16, 16, 6, 21, 9, 12, 9, 15, 10, 20, 9, 22, 9, 17, 7, 31, 7, 11, 13, 21, 9, 17, 11, 16, 14, 21, 5, 32, 7, 12, 16

Offset: 1

Reinhard Zumkeller, Mar 24 2002

nonn

			A000040(8)^8-1 = 19^8 - 1 = 16983563040 = 2^5*3^2*5*17*181*3833, therefore a(8) = 6 and A069462(8) = 11.
A000040(9)^9-1 = 23^9-1 = 1801152661462 = 2*7*11*19*79*7792003, therefore a(9) = 6 and A069462(9) = 6.

Amiram Eldar, Table of n, a(n) for n = 1..96 (using factordb.com)
Dario Alpern, Factorization using the Elliptic Curve Method.
FactorDB, Status of 509^97-1.

Cf. A001221, A069459, A069462, A069464.

Table[PrimeNu[Prime[n]^n - 1], {n, 1, 30}] (* Amiram Eldar, Feb 17 2020 *)

for(n=1,52,print1(omega(prime(n)^n-1)",")) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 03 2008

a(n) = A001221(A069459(n)).

More terms from Hugo Pfoertner, May 18 2004
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 03 2008
a(53)-a(75) using factordb.com from Amiram Eldar, Feb 17 2020

A069462 Number of prime factors of prime(n)^n-1, with multiplicity.

Original entry on oeis.org

0, 3, 3, 8, 4, 8, 5, 11, 6, 11, 7, 16, 7, 10, 9, 15, 5, 16, 4, 19, 12, 14, 4, 24, 11, 15, 15, 19, 9, 23, 5, 22, 12, 10, 11, 26, 9, 14, 8, 22, 5, 26, 5, 22, 18, 21, 6, 30, 9, 16, 11, 24, 13, 28, 17, 27, 10, 23, 8, 37, 7, 14, 16, 29, 12, 20, 11, 22, 14, 26, 9, 40

Offset: 1

Reinhard Zumkeller, Mar 24 2002

nonn

			A000040(8)^8-1 = 19^8-1 = 16983563040 = 2^5*3^2*5*17*181*3833, therefore a(8) = 11 and A069461(8) = 6.
A000040(9)^9-1 = 23^9-1 = 1801152661462 = 2*7*11*19*79*7792003, therefore a(9) = 6 and A069461(9) = 6.

Amiram Eldar, Table of n, a(n) for n = 1..96 (using factordb.com)
Dario Alpern, Factorization using the Elliptic Curve Method.
FactorDB, Status of 509^97-1.

Cf. A001222, A069459, A069461, A069465.

Table[PrimeOmega[Prime[n]^n - 1], {n, 1, 30}] (* Amiram Eldar, Feb 17 2020 *)

for(n=1,52,print1(bigomega(prime(n)^n-1)",")) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 03 2008

a(n) = A001222(A069459(n)).

More terms from Hugo Pfoertner, May 21 2004
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 03 2008
a(53)-a(72) using factordb.com from Amiram Eldar, Feb 17 2020

A319074 a(n) is the sum of the first n nonnegative powers of the n-th prime.

Original entry on oeis.org

1, 4, 31, 400, 16105, 402234, 25646167, 943531280, 81870575521, 15025258332150, 846949229880161, 182859777940000980, 23127577557875340733, 1759175174860440565844, 262246703278703657363377, 74543635579202247026882160, 21930887362370823132822661921, 2279217547342466764922495586798

Offset: 1

Omar E. Pol, Sep 11 2018

nonn

			For n = 4 the 4th prime is 7 and the sum of the first four nonnegative powers of 7 is 7^0 + 7^1 + 7^2 + 7^3 = 1 + 7 + 49 + 343 = 400, so a(4) = 400.

Main diagonal of A319076.
Cf. A000040, A000203, A006093, A062457, A069459, A093360, A319075.
Cf. A000079, A000244, A000351, A000420, A001020, A001022, A001026, A001029, A009967, A009973, A009975, A009981, A009985, A009987, A009991.
Cf. A126646, A003462, A003463, A023000, A016123, A091030, A091045, A218722, A218726, A218732, A218734, A218740, A218744, A218746, A218750.

a(n) = sum(k=0, n-1, prime(n)^k); \\ Michel Marcus, Sep 13 2018

a(n) = Sum_{k=0..n-1} A000040(n)^k.
a(n) = Sum_{k=0..n-1} A319075(k,n).
a(n) = (A000040(n)^n - 1)/(A000040(n) - 1).
a(n) = (A062457(n) - 1)/A006093(n).
a(n) = A069459(n)/A006093(n).
a(n) = A000203(A000040(n)^(n-1)).
a(n) = A000203(A093360(n)).

cp's OEIS Frontend

A069460 Greatest prime factor of prime(n)^n - 1.

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A069461 Number of distinct prime factors of prime(n)^n-1.

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Author

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Mathematica

PARI

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A069462 Number of prime factors of prime(n)^n-1, with multiplicity.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula

Extensions

A319074 a(n) is the sum of the first n nonnegative powers of the n-th prime.

Views

Author

Keywords

Examples

Crossrefs

Programs

PARI

Formula