A277128 Values of n such that A019530(n) is different from A007947(n).

1, 8, 16, 32, 64, 81, 128, 243, 256, 384, 512, 729, 768, 1024, 1152, 1536, 2048, 2187, 2304, 3072, 3456, 4096, 4374, 4608, 6144, 6561, 6912, 8192, 8748, 9216, 10240, 10368, 12288, 13122, 13824, 15625, 16384, 17496, 18432, 19683, 20480, 20736, 24576, 26244, 27648

Offset

1,2

Comments

For primes p, p^k is in the sequence for k > p. More generally, if n is in the sequence, p*n is for some prime p|n.

Links

Table of n, a(n) for n=1..45.

Example

8 is in the sequence because m^m isn't divisible by 8, where m is the kernel of 8 = A007947(8) = 2. I.e. 2^2 isn't divisible by 8.
4374 = 2 * 3^7 is in the sequence because there is some exponent e in the prime factorization such that e > A007947(4374) = 6.

Mathematica

max = 10^4; A007947[n_] := Times @@ (FactorInteger[n][[All, 1]]); A019530[1] = 0; A019530[n_] := For[m = 2, True, m++, If[PowerMod[m, m, n] == 0, Return[m]]]; Reap[For[n = 1, n < max, n++, If[A007947[n] != A019530[n], Print[n]; Sow[n]]]][[2, 1]]

Prog

(PARI) A007947(n) = factorback(factorint(n)[, 1]);
is(n) = my(m=A007947(n)); Mod(m, n)^m!=0;

Crossrefs

Cf. A007947, A019530.

Sequence in context: A303026 A068935 A371011 * A054743 A192135 A345053

Adjacent sequences: A277125 A277126 A277127 * A277129 A277130 A277131

Keyword

nonn

Author

Jean-François Alcover and David A. Corneth, Oct 01 2016

Status

approved