A076333 -id:A076333 - cp's OEIS frontend

A118669 Numbers that are not squarefree, but contain their squarefree kernel in decimal representation.

25, 32, 36, 96, 100, 125, 128, 162, 216, 243, 256, 300, 486, 512, 576, 625, 648, 700, 768, 864, 1000, 1024, 1100, 1215, 1296, 1300, 1536, 1700, 1900, 2048, 2100, 2300, 2430, 2900, 2916, 3000, 3100, 3125, 3300, 3456, 3700, 3773, 3900, 4100, 4300, 4608

Offset: 1

Reinhard Zumkeller, May 19 2006

For k>1: m*10^k are terms for squarefree numbers m coprime to 10.

If m is a term and coprime to 10 then also 10*m is a term.

Amiram Eldar, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Squarefree.

Cf. A005117, A013929, A007947, A076333.

Select[Range[5000], (r = rad[#]) < # && SequenceCount @@ IntegerDigits[{#, r}] > 0 &] (* Amiram Eldar, Sep 07 2020 *)

A076619 Least x>1 such that x^d == 1 (mod d) for each divisor d of n, for all nonsquarefree numbers n (cf. A013929).

Original entry on oeis.org

3, 3, 4, 7, 3, 7, 11, 7, 6, 4, 15, 3, 7, 11, 23, 16, 7, 8, 11, 27, 7, 15, 31, 22, 3, 35, 7, 16, 39, 11, 4, 43, 23, 31, 47, 7, 15, 34, 11, 27, 7, 15, 59, 40, 31, 12, 63, 6, 43, 3, 67, 16, 35, 71, 7, 22, 75, 31, 39, 52, 79, 11, 7, 83, 43, 14, 58, 87, 36, 23, 31, 47, 95, 22, 7, 15, 67

Offset: 1

Benoit Cloitre, Oct 22 2002

nonn

If n is squarefree (cf. A005117), then the least x>1 such that x^d == 1 (mod d) (for each divisor d of n) equals n+1.

Cf. A013929, A076333, A076618 (sequence for all integers).

f[n_] := If[(r = Times @@ FactorInteger[n][[;; , 1]]) < n, r, 0]; Select[f /@ Range[200], # > 0 &] + 1 (* Amiram Eldar, Feb 11 2021 *)

lista(nn) = {for(n=1, nn, if (!issquarefree(n), print1(A076618(n), ", ");););} \\ Michel Marcus, Jul 13 2013

a(p^m) = p+1 for p prime and m>1.
a(n) = A076618(A013929(n)). - Michel Marcus, Jul 13 2013
a(n) = A076333(n) + 1. - Amiram Eldar, Feb 11 2021

cp's OEIS Frontend

A118669 Numbers that are not squarefree, but contain their squarefree kernel in decimal representation.

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