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 A062770 n/[largest power of squarefree kernel] equals 1; perfect powers of sqf-kernels (or sqf-numbers). 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 (list; graph; refs; listen; history; text; internal format)
 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 Michael De Vlieger, Table of n, a(n) for n = 1..10000 FORMULA A062760(a(n)) = 1, i.e., a(n)/(A007947(a(n))^A051904(a(n))) = a(n))/A062759(a(n)) = 1. EXAMPLE Primes, squarefree numbers and perfect powers are here. From Michael De Vlieger, Jun 24 2022 (Start): 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 (PARI) is(n)=ispower(n, , &n); issquarefree(n) && n>1 \\ Charles R Greathouse IV, Sep 18 2015 (PARI) is(n)=#Set(factor(n)[, 2])==1 \\ Charles R Greathouse IV, Sep 18 2015 CROSSREFS Cf. A062759, A062760, A007947, A003557, A051904, A005117, A001597. Sequence in context: A360249 A360247 A072774 * A359889 A236510 A317710 Adjacent sequences: A062767 A062768 A062769 * A062771 A062772 A062773 KEYWORD nonn AUTHOR Labos Elemer, Jul 18 2001 EXTENSIONS Offset corrected by Charles R Greathouse IV, Sep 18 2015 STATUS approved

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Last modified April 23 19:56 EDT 2024. Contains 371916 sequences. (Running on oeis4.)