A318956 For any number n > 0 with prime factorization Product_{k=1..w} p_k ^ x_k (where p_1 < p_2 < ... < p_w and x_k > 0 for k=1..w), let (o_1, ..., o_w) be the ordinal transform of (x_1, ..., x_w); a(n) = Product_{k=1..w} p_k ^ o_k.

1, 2, 3, 2, 5, 18, 7, 2, 3, 50, 11, 6, 13, 98, 75, 2, 17, 6, 19, 10, 147, 242, 23, 6, 5, 338, 3, 14, 29, 2250, 31, 2, 363, 578, 245, 18, 37, 722, 507, 10, 41, 6174, 43, 22, 15, 1058, 47, 6, 7, 10, 867, 26, 53, 6, 605, 14, 1083, 1682, 59, 150, 61, 1922, 21, 2

Offset: 1

Author

Rémy Sigrist, Sep 20 2018

Keywords

• nonn

Comments

The ordinal transform of a sequence b(n) is the sequence t(n) = number of values in b(1), ..., b(n) which are equal to b(n).

Crossrefs

Cf. A002110, A005117, A076954, A130091.

Programs

PARI

a(n) = if (n==1, 1, my (f=factor(n), o=vector(vecmax(f[,2]))); for (i=1, #f~, f[i,2] = o[f[i,2]]++); factorback(f))

Formula

a(p) = p iff p = 1 or p is prime.

a(n^k) = a(n) for any n > 0 and k > 0.

A007947(a(n)) = A007947(n) for any n > 0.

a(a(a(n))) = a(n) for any n > 0.

a(n) belongs to A005117 iff n belongs to A130091 and vice versa.

a(A002110(n)) = A076954(n) for any n >= 0.

a(A076954(n)) = A002110(n) for any n >= 0.