A336063 Numbers divisible by the minimal exponent in their prime factorization (A051904).

2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74

Offset: 1

Author

Amiram Eldar, Jul 07 2020

Keywords

• nonn

Comments

The asymptotic density of this sequence is 1 (Schinzel and Šalát, 1994).

Examples

			4 = 2^2 is a term since A051904(4) = 2 is a divisor of 4.
		

References

• József Sándor and Borislav Crstici, Handbook of Number theory II, Kluwer Academic Publishers, 2004, chapter 3, p. 331.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Andrzej Schinzel and Tibor Šalát, Remarks on maximum and minimum exponents in factoring, Mathematica Slovaca, Vol. 44, No. 5 (1994), pp. 505-514.

Crossrefs

Cf. A051904, A124184.

A005117 (except for 1) is subsequence.

Similar sequences: A033950, A005349, A006446, A074946, A075592, A007694, A112249, A336064.

Programs

Mathematica

h[1] = 0; h[n_] := Min[FactorInteger[n][[;; , 2]]]; Select[Range[2, 100], Divisible[#, h[#]] &]
Select[Range[2,100],Divisible[#,Min[FactorInteger[#][[All,2]]]]&] (* Harvey P. Dale, Aug 31 2020 *)

PARI

isok(m) = if (m>1, (m % vecmin(factor(m)[,2])) == 0); \\ Michel Marcus, Jul 08 2020