A071350 -id:A071350 - cp's OEIS frontend

A071349 Numbers k for which the GCD of the k-th primorial number and its totient (A058250) sets record.

1, 2, 4, 5, 9, 10, 15, 16, 17, 23, 27, 28, 35, 39, 40, 41, 43, 49, 56, 57, 61, 62, 64, 66, 69, 72, 73, 76, 77, 91, 92, 96, 97, 102, 103, 104, 107, 111, 114, 117, 119, 127, 128, 137, 139, 143, 146, 150, 154, 155, 166, 171, 181, 182, 186, 195, 196, 201, 208, 214, 215

Offset: 1

Labos Elemer, May 21 2002

nonn

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

Cf. A058250, A002110, A000010, A005867, A071350.

q[n_] := Product[Prime[i], {i, 1, n}]; fq[n_] := Product[Prime[i] - 1, {i, 1, n}];
a=0; Do[s=GCD[q[n], fq[n]]; If[s>a, a=s; Print[n]], {n, 1, 1000}]

If A058250(m) > A058250(k) for all k < m then m is a term.

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

A071349 Numbers k for which the GCD of the k-th primorial number and its totient (A058250) sets record.

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