A226872 -id:A226872 - cp's OEIS frontend

A228870 Numbers n such that 2 * (1^n + 2^n + 3^n + ... + n^n) is not 0 (mod n).

6, 12, 18, 20, 24, 30, 36, 40, 42, 48, 54, 60, 66, 72, 78, 80, 84, 90, 96, 100, 102, 108, 110, 114, 120, 126, 132, 138, 140, 144, 150, 156, 160, 162, 168, 174, 180, 186, 192, 198, 200, 204, 210, 216, 220, 222, 228, 234, 240, 246, 252, 258, 260, 264, 270, 272

Offset: 1

T. D. Noe, Sep 06 2013

nonn

These are the numbers not appearing in A228869; the even numbers not in A226872.
Also, positive integers n such that there exists an odd prime divisor p of n such that (p-1) also divides n (cf. A124240). - Max Alekseyev, Sep 07 2013
This sequence agrees with A088723 for many terms, but they are different.
If n is in the sequence, then so are the multiples of n. See A280187 for primitive members of this sequence. - Charles R Greathouse IV, Dec 28 2016

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A228869, A226872.

Select[Range[100], Mod[2*Sum[PowerMod[k, #, #], {k, #}], #] > 0 &]

is(n)=my(f=factor(n)[,1]); for(i=1,#f, if(n%(f[i]-1)==0 && f[i]>2, return(1))); 0 \\ Charles R Greathouse IV, Dec 28 2016

A228869 Numbers n such that 2 * (1^n + 2^n + 3^n + ... + n^n) == 0 (mod n).

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 37, 38, 39, 41, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 79, 81, 82, 83

Offset: 1

T. D. Noe, Sep 06 2013

nonn

See A228870 for the numbers not in this sequence.
Union of A226872 and the positive odd integers (A005408).
Also, positive integers n such that (p-1) does not divide n for every odd prime p dividing n (cf. A124240). - Max Alekseyev, Sep 07 2013

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A228870, A226872.

Select[Range[100], Mod[2*Sum[PowerMod[k, #, #], {k, #}], #] == 0 &]

A225821 a(n) = Product_{p | p is prime and p, p-1 both divide n}.

Original entry on oeis.org

1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 6, 1, 10, 1, 2, 1, 6, 1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 6, 1, 2, 1, 10, 1, 42, 1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 30, 1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 6, 1, 10, 1, 2, 1, 42

Offset: 1

José María Grau Ribas, Jul 30 2013

nonn

a(n) = 2 iff n is even and is a term of A226872. - Daniel Suteu, Jul 28 2019
From Bernard Schott, Jul 30 2019: (Start)
a(n) = n if n = 1, 2, 6, 42, 1806.
a(n) = 6 if n is of the form 2^i*3^j, i and j >= 1, so if n is a term of A033845.
a(n) = 10 if n is of the form 2^i*5^j, i >= 2 and j >= 1.
a(n) = 30 if n is of the form 2^i*3^j*5^k, i >=2, j >= 1 and k >= 1. (End)

Eric M. Schmidt, Table of n, a(n) for n = 1..10000

Cf. A173557, A027760.

fa=FactorInteger; d[m_]:= Product[If[IntegerQ[m/(fa[m][[i, 1]]-1)],fa[m][[i, 1]], 1], {i, Length@fa@m}]; Table[d[n], {n, 1, 333}]

a(n)=my(f=factor(n)[,1]); prod(i=1,#f,if(n%(f[i]-1)==0,f[i],1)) \\ Charles R Greathouse IV, Nov 13 2013

def A225821(n) : return prod(p for (p,m) in factor(n) if n%(p-1)==0) # Eric M. Schmidt, Jul 31 2013

a(n) = denominator(A031971(n)/n) = gcd(n, A027642(n)). - Daniel Suteu, Jul 28 2019

cp's OEIS Frontend

A228870 Numbers n such that 2 * (1^n + 2^n + 3^n + ... + n^n) is not 0 (mod n).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

A228869 Numbers n such that 2 * (1^n + 2^n + 3^n + ... + n^n) == 0 (mod n).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A225821 a(n) = Product_{p | p is prime and p, p-1 both divide n}.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Sage

Formula