A172418 -id:A172418 - cp's OEIS frontend

A172419 Numbers k that have measure of smoothness J larger than 4, where J = log(k)/log(rad(k)) and rad(k) is the product of the distinct prime divisors of k (A007947).

32, 64, 128, 243, 256, 512, 729, 1024, 1458, 1536, 1728, 1944, 2048, 2187, 2304, 2592, 2916, 3072, 3125, 3456, 3888, 4096, 4374, 4608, 5184, 5832, 6144, 6561, 6912, 7776, 8192, 8748, 9216, 10240, 10368, 11664, 12288, 12500, 12800, 13122, 13824, 15552

Offset: 1

Artur Jasinski, Feb 02 2010

nonn

Subsequence of A049094 and A172418.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A007947, A049094, A172418, A172420, A172421, A172422.

aa = {}; Do[kk = FactorInteger[c]; nn = 1; Do[nn = nn*kk[[n]][[1]], {n, 1, Length[kk]}]; If[Log[c]/Log[nn] > 4, AppendTo[aa, c]], {c, 2, 10000}]; aa

A172420 Numbers k that have measure of smoothness J larger than 5, where J = log(k)/log(rad(k)) and rad(k) is the product of the distinct prime divisors of k (A007947).

Original entry on oeis.org

64, 128, 256, 512, 729, 1024, 2048, 2187, 4096, 6561, 8192, 8748, 9216, 10368, 11664, 12288, 13122, 13824, 15552, 15625, 16384, 17496, 18432, 19683, 20736, 23328, 24576, 26244, 27648, 31104, 32768, 34992, 36864, 39366, 41472, 46656, 49152

Offset: 1

Artur Jasinski, Feb 02 2010

nonn

This sequence is a subsequence of A049094, A172418, and A172419.

Amiram Eldar, Table of n, a(n) for n = 1..3000 (terms 1..368 from Harvey P. Dale)

Cf. A007947, A049094, A059172, A172418, A172419, A172421, A172422.

aa = {}; Do[kk = FactorInteger[c]; nn = 1; Do[nn = nn*kk[[n]][[1]], {n, 1, Length[kk]}]; If[Log[c]/Log[nn] > 5, AppendTo[aa, c]], {c, 2, 10000}]; aa
Select[Range[2,50000],Log[Times@@FactorInteger[#][[All,1]],#]>5&] (* Harvey P. Dale, Apr 30 2018 *)

A172421 Numbers k that have measure of smoothness J larger than 6, where J = log(k)/log(rad(k)) and rad(k) is the product of the distinct prime divisors of k (A007947).

Original entry on oeis.org

128, 256, 512, 1024, 2048, 2187, 4096, 6561, 8192, 16384, 19683, 32768, 49152, 52488, 55296, 59049, 62208, 65536, 69984, 73728, 78125, 78732, 82944, 93312, 98304, 104976, 110592, 118098, 124416, 131072, 139968, 147456, 157464, 165888, 177147, 186624, 196608

Offset: 1

Artur Jasinski, Feb 02 2010

nonn

This sequence is a subsequence of A049094, A172418, A172419, and A172420.

Amiram Eldar, Table of n, a(n) for n = 1..1000

Cf. A007947, A049094, A059172, A172418, A172419, A172420, A172422.

aa = {}; Do[kk = FactorInteger[c]; nn = 1; Do[nn = nn*kk[[n]][[1]], {n, 1, Length[kk]}]; If[Log[c]/Log[nn] > 6, AppendTo[aa, c]], {c, 2, 10000}]; aa

More terms from Amiram Eldar, Mar 10 2020

A172422 Numbers k that have measure of smoothness J larger than 7, where J = log(k)/log(rad(k)) and rad(k) is the product of the distinct prime divisors of k (A007947).

Original entry on oeis.org

256, 512, 1024, 2048, 4096, 6561, 8192, 16384, 19683, 32768, 59049, 65536, 131072, 177147, 262144, 294912, 314928, 331776, 354294, 373248, 390625, 393216, 419904, 442368, 472392, 497664, 524288, 531441, 559872, 589824, 629856, 663552, 708588, 746496, 786432

Offset: 1

Artur Jasinski, Feb 02 2010

nonn

This sequence is a subsequence of A049094, A172418, A172419, A172420, and A172421.

Amiram Eldar, Table of n, a(n) for n = 1..500

Cf. A007947, A049094, A059172, A172418, A172419, A172420, A172421.

aa = {}; Do[kk = FactorInteger[c]; nn = 1; Do[nn = nn*kk[[n]][[1]], {n, 1, Length[kk]}]; If[Log[c]/Log[nn] > 7, AppendTo[aa, c]], {c, 2, 10000}]; aa

More terms from Amiram Eldar, Mar 10 2020

cp's OEIS Frontend

A172419 Numbers k that have measure of smoothness J larger than 4, where J = log(k)/log(rad(k)) and rad(k) is the product of the distinct prime divisors of k (A007947).

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A172420 Numbers k that have measure of smoothness J larger than 5, where J = log(k)/log(rad(k)) and rad(k) is the product of the distinct prime divisors of k (A007947).

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A172421 Numbers k that have measure of smoothness J larger than 6, where J = log(k)/log(rad(k)) and rad(k) is the product of the distinct prime divisors of k (A007947).

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A172422 Numbers k that have measure of smoothness J larger than 7, where J = log(k)/log(rad(k)) and rad(k) is the product of the distinct prime divisors of k (A007947).

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