A077066 -id:A077066 - cp's OEIS frontend

A077063 Squarefree kernel of prime(n) - 1.

1, 2, 2, 6, 10, 6, 2, 6, 22, 14, 30, 6, 10, 42, 46, 26, 58, 30, 66, 70, 6, 78, 82, 22, 6, 10, 102, 106, 6, 14, 42, 130, 34, 138, 74, 30, 78, 6, 166, 86, 178, 30, 190, 6, 14, 66, 210, 222, 226, 114, 58, 238, 30, 10, 2, 262, 134, 30, 138, 70, 282, 146, 102, 310, 78, 158

Offset: 1

Reinhard Zumkeller, Oct 23 2002

nonn

			a(25) = rad(prime(25)-1) = rad(97-1) = rad(3*2^5) = 6.

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

Cf. A006093, A007947, A077066.

a077063 = a007947 . a006093  -- Reinhard Zumkeller, Sep 04 2013

A077063 := proc(n)
    A007947(A006093(n)) ;
end proc:
seq(A077063(n),n=1..30) ; # R. J. Mathar, Jan 13 2021

rad[n_] := Times @@ (First@# & /@ FactorInteger[n]); rad /@
Select[Range[400], PrimeQ[# + 1] &] (* Amiram Eldar, Dec 29 2020 *)
Times@@FactorInteger[#-1][[;;,1]]&/@Prime[Range[70]] (* Harvey P. Dale, Mar 16 2023 *)

a(n)=my(f=factor(prime(n)-1)[,1]); prod(i=1,#f,f[i]) \\ Charles R Greathouse IV, Aug 21 2013

a(n) = A007947(A006093(n)).

Wrong formula removed by Amiram Eldar, Dec 29 2020

A077067 Squarefree numbers of the form prime + 1.

Original entry on oeis.org

3, 6, 14, 30, 38, 42, 62, 74, 102, 110, 114, 138, 158, 174, 182, 194, 230, 258, 278, 282, 314, 318, 354, 374, 390, 398, 402, 410, 422, 434, 458, 462, 510, 542, 570, 602, 614, 618, 642, 654, 662, 674, 678, 710, 734, 758, 762, 770, 798, 822, 830, 854, 858, 878

Offset: 1

Reinhard Zumkeller, Oct 23 2002

nonn

			A005117(28) = 42 = 2*3*7 is a term as 42 = A000040(13) + 1 = 41+1.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A000040, A005117, A008864, A049097, A077064, A077066.

Select[Prime[Range[200]]+1,SquareFreeQ] (* Harvey P. Dale, Aug 20 2017 *)

isok(n) = issquarefree(n) && isprime(n-1); \\ Michel Marcus, Mar 22 2016

lista(nn) = forprime(p=2, nn, if (issquarefree(p+1), print1(p+1, ", "))); \\ Michel Marcus, Mar 22 2016

A077066(a(n)) = a(n).

a(n) = A049097(n)+1. - Zak Seidov, Aug 15 2006

A275630 a(n) = product of distinct primes dividing prime(n)^2 - 1.

Original entry on oeis.org

3, 2, 6, 6, 30, 42, 6, 30, 66, 210, 30, 114, 210, 462, 138, 78, 870, 930, 1122, 210, 222, 390, 1722, 330, 42, 510, 1326, 318, 330, 798, 42, 4290, 2346, 4830, 1110, 570, 6162, 246, 3486, 7482, 2670, 2730, 570, 582, 462, 330, 11130, 1554, 12882, 13110, 2262, 3570, 330, 210, 258, 8646, 2010

Offset: 1

N. J. A. Sloane, Aug 07 2016

nonn

Amiram Eldar, Table of n, a(n) for n = 1..10000

Subsequence of A007947.

Cf. A077063, A077066, A084920.

a[n_] := Times @@ FactorInteger[Prime[n]^2 - 1][[;; , 1]]; Array[a, 60] (* Amiram Eldar, Jan 30 2021 *)

a(n) = factorback(factorint(prime(n)^2-1)[, 1]); \\ Michel Marcus, Jan 30 2021

a(n) = A007947(A084920(n)). - Michel Marcus, Jan 30 2021

a(n) = A077063(n)*A077066(n)/2, for n > 1. - Amiram Eldar, Jan 30 2021

cp's OEIS Frontend

A077063 Squarefree kernel of prime(n) - 1.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Haskell

Maple

Mathematica

PARI

Formula

Extensions

A077067 Squarefree numbers of the form prime + 1.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI

PARI

Formula

A275630 a(n) = product of distinct primes dividing prime(n)^2 - 1.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula