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

1,1

Comments

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

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.

Example

4 = 2^2 is a term since A051903(4) = 2 is a divisor of 4.

Mathematica

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

Prog

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

Crossrefs

Cf. A051903, A124184, A336065.

A005117 (except for 1) is subsequence.

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

Sequence in context: A031981 A279486 A336063 * A039269 A039207 A272576

Adjacent sequences: A336061 A336062 A336063 * A336065 A336066 A336067

Keyword

nonn

Author

Amiram Eldar, Jul 07 2020

Status

approved