A353693 -id:A353693 - cp's OEIS frontend

A353695 Indices of records in A353693.

1, 6, 15, 30, 70, 105, 210, 462, 770, 1155, 2145, 2310, 4290, 6006, 9282, 10010, 15015, 23205, 30030, 46410, 67830, 72930, 102102, 149226, 170170, 248710, 255255, 373065, 440895, 510510, 746130, 881790, 1193010, 1385670, 1874730, 1939938, 2624622, 3233230

Offset: 1

Amiram Eldar, May 04 2022

nonn

The corresponding record values are 1, 2, 3, 12, 20, 45, 360, 504, 1400, 4725, 7425, 75600, 118800, 232848, 275184, 1078000, 5457375, 6449625, 174636000, 206388000, 269892000, 509652000, ...

Are all the terms squarefree (A005117)? If yes, then the calculation of terms of this sequence can be significantly sped up.

			The first 15 terms of A353693 are 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2 and 3. The record values, 1, 2 and 3, occur at 1, 6 and 15, the first 3 terms of this sequence.

Chai Wah Wu, Table of n, a(n) for n = 1..51

Cf. A005117, A353693.

f[n_] := Module[{k = 1}, While[! UnsameQ @@ FactorInteger[k*n][[;; , 2]], k++]; k]; fm = 0; s = {}; Do[f1 = f[n]; If[f1 > fm, fm = f1; AppendTo[s, n]], {n, 1, 10^4}]; s

a(27)-a(38) from Chai Wah Wu, May 07 2022

A353694 a(n) is the least multiple of n with mutually distinct exponents in its prime factorization (A130091).

Original entry on oeis.org

1, 2, 3, 4, 5, 12, 7, 8, 9, 20, 11, 12, 13, 28, 45, 16, 17, 18, 19, 20, 63, 44, 23, 24, 25, 52, 27, 28, 29, 360, 31, 32, 99, 68, 175, 72, 37, 76, 117, 40, 41, 504, 43, 44, 45, 92, 47, 48, 49, 50, 153, 52, 53, 54, 275, 56, 171, 116, 59, 360, 61, 124, 63, 64, 325

Offset: 1

Amiram Eldar, May 04 2022

nonn

			a(2) = 2 since 2 = 2^1 has only one exponent (1) in its prime factorization.
a(6) = 12 since 6 = 2*3 has two equal exponents (1) in its prime factorization, and 2*6 = 12 = 2^2*3 has two distinct exponents (1 and 2).

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

Cf. A130091, A130092, A353693.

a[n_] := Module[{k = n}, While[!UnsameQ @@ FactorInteger[k][[;; , 2]], k += n]; k]; Array[a, 100]

a(n) = n if and only if n is in A130091.
a(A130092(n)) > n.
a(n) = n * A353693(n).

cp's OEIS Frontend

A353695 Indices of records in A353693.

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