

A062770


n/[largest power of squarefree kernel] equals 1; perfect powers of sqfkernels (or sqfnumbers).


19



2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 46, 47, 49, 51, 53, 55, 57, 58, 59, 61, 62, 64, 65, 66, 67, 69, 70, 71, 73, 74, 77, 78, 79, 81, 82, 83, 85, 86, 87, 89, 91, 93, 94, 95, 97, 100
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OFFSET

1,1


COMMENTS

The sequence contains numbers m such that the exponents e are identical for all prime power factors p^e  m. It is clear from this alternate definition that m / K^E = 1 iff E is an integer.  Michael De Vlieger, Jun 24 2022


LINKS



FORMULA



EXAMPLE

Primes, squarefree numbers and perfect powers are here.
144 cannot be in the sequence, since the exponents of its prime power factors differ. The squarefree kernel of 144 = 2^4 * 3^2 is 2*3 = 6. The largest power of 6 less than 144 is 36. 144/36 = 4, so it is not in the sequence.
216 is in the sequence because 216 = 2^3 * 3^3 is 2*3 = 6. But 216 = 6^3, hence 6^3 / 6^3 = 1. (End)


MATHEMATICA

Select[Range[2, 2^16], Length@ Union@ FactorInteger[#][[All, 1]] == 1 &] Michael De Vlieger, Jun 24 2022


PROG



CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



