A354932 a(n) = 1/n * {the least k for which A345992(k) = n}.

1, 3, 4, 5, 3, 7, 4, 3, 5, 11, 3, 13, 7, 5, 4, 7, 3, 19, 4, 7, 11, 9, 3, 7, 13, 9, 4, 17, 3, 31, 4, 3, 17, 5, 9, 31, 5, 11, 5, 9, 3, 17, 4, 5, 13, 31, 3, 7, 5, 17, 4, 19, 3, 5, 7, 19, 23, 9, 3, 61, 8, 7, 8, 5, 11, 19, 4, 23, 7, 47, 3, 29, 7, 5, 19, 9, 13, 47, 4, 7, 13, 11, 3, 17, 16, 23, 4, 23, 3, 13, 4, 31, 11, 5

Offset: 1

Author

Antti Karttunen, Jun 14 2022

Keywords

• nonn

Comments

The first four terms that are not powers of primes are: a(112) = 15, a(122) = 35, a(145) = 33, a(155) = 12.

Question: Are 2, 3, 4, 6, 10, 12, 18, 30, 60 the only n such that a(n) = 1+n?

Links

• Antti Karttunen, Table of n, a(n) for n = 1..3349 (computed using million term data file provided for A344005 by _N. J. A. Sloane_)

Crossrefs

Column 1 of A354940.

Cf. A344005, A345992, A354931.

Programs

Mathematica

s[n_] := Module[{m = 1}, While[!Divisible[m*(m+1), n], m++]; GCD[n, m]]; a[n_] := Module[{k = n}, While[s[k] != n, k+=n]; k/n]; Array[a, 100] (* Amiram Eldar, Jun 15 2022 *)

PARI

A345992(n) = gcd(n,A344005(n));
A354932(n) = for(k=1,oo,if(A345992(k)==n,return(k/n)));

Formula

a(n) = A354931(n) / n.