A336064 Numbers divisible by the maximal exponent in their prime factorization (A051903).

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, 41, 42, 43, 44, 46, 47, 48, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 76, 77, 78, 79

Offset: 1

Author

Amiram Eldar, Jul 07 2020

Keywords

• nonn

Comments

The asymptotic density of this sequence is A336065 = 0.848957... (Schinzel and Šalát, 1994).

Examples

			4 = 2^2 is a term since A051903(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. A051903, A124184, A336065.

A005117 (except for 1) is subsequence.

Similar sequences: A033950, A005349, A006446, A074946, A075592, A007694, A112249, A336063.

Programs

Mathematica

H[1] = 0; H[n_] := Max[FactorInteger[n][[;; , 2]]]; Select[Range[2, 100], Divisible[#, H[#]] &]

PARI

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