A071349 -id:A071349 - cp's OEIS frontend

A071350 Distinct values of A058250; these terms appear first at subscripts listed in A071349.

1, 2, 6, 30, 330, 2310, 53130, 690690, 20030010, 821230410, 13960916970, 739928599410, 27377358178170, 2272320728788110, 97709791337888730, 8696171429072096970, 165227257152369842430, 18670680058217792194590

Offset: 1

Labos Elemer, May 21 2002

Michael De Vlieger, Table of n, a(n) for n = 1..341

Cf. A058250, A002110, A000010, A005867, A071349, A112037.

Prepend[FoldList[Times,DeleteDuplicates[Rest[Flatten[FactorInteger[#][[All, 1]]&/@(Prime[Range[100]]-1)]]]],1] (* Jamie Morken, Apr 27 2021 after Harvey P. Dale at A112037, May 26 2019 *)

f(n) = my(pr=prod(k=1, n, prime(k))); gcd(pr, eulerphi(pr)); \\ A058250
lista(nn) = Set(vector(nn, k, f(k))); \\ Michel Marcus, Apr 27 2021

a(n) = a(n-1) * A112037(n), n >= 2. - David A. Corneth, Apr 27 2021

A307805 a(n) = first position of prime(n) in A023503.

Original entry on oeis.org

2, 4, 5, 10, 9, 16, 27, 43, 15, 17, 64, 35, 23, 40, 61, 28, 127, 73, 57, 104, 62, 66, 39, 41, 77, 111, 114, 117, 182, 49, 97, 56, 143, 102, 196, 155, 248, 119, 346, 69, 72, 181, 76, 137, 497, 139, 318, 388, 721, 401, 91, 92, 229, 96, 243, 249, 325, 258, 186, 103

Offset: 1

Michael De Vlieger, Apr 29 2019

nonn

A023503(n) = A006530(A006093(n)).
Apparent permutation of A071349(n) apart from A071349(1) = 1.
Let i = a(n). Sorting prime(n) in order of increasing i yields A112037 = {2, 3, 5, 11, 7, 23, 13, 29, 41, ...}. The product of the first j terms of A112037 = A071350(j).

			a(1) = 2 since prime(1) = gpf(prime(2) - 1), i.e., 2 = gpf(2).
a(2) = 4 since prime(2) = gpf(prime(4) - 1), i.e., 3 = gpf(6).
a(3) = 5 since prime(3) = gpf(prime(5) - 1), i.e., 5 = gpf(10).
a(4) = 10 since prime(4) = gpf(prime(10) - 1), i.e., 7 = gpf(28).

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Cf. A006093, A006530, A023503, A071349, A112037.

With[{s = Array[FactorInteger[Prime@ # - 1][[-1, 1]] &, 1000]}, Reap[Do[If[FreeQ[s, #], Break[], Sow@ FirstPosition[s, #][[1]]] &@ Prime@ i, {i, Length@ s}]][[-1, -1]]]

{ a = vector(60); pr = primes(#a); u = 1; n = 1;
forprime (p=3, oo, n++; f=factor(p-1); g=setsearch(pr, f[#f~,1]);
if (g && !a[g], a[g]=n; while (a[u], print1 (a[u]", "); u++; if (u>#a, break (2))))) } \\ Rémy Sigrist, May 28 2019

cp's OEIS Frontend

A071350 Distinct values of A058250; these terms appear first at subscripts listed in A071349.

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