A382408 a(n) is the number of terms in A071174 whose radical is A144338(n).

1, 1, 1, 5, 1, 9, 1, 1, 13, 14, 1, 1, 20, 21, 1, 25, 1, 406, 1, 32, 33, 34, 1, 37, 38, 1, 820, 1, 45, 1, 50, 1, 54, 56, 57, 1, 1, 61, 64, 2080, 1, 68, 2346, 1, 1, 73, 76, 2926, 1, 81, 1, 84, 85, 86, 1, 90, 92, 93, 94, 1, 1, 5050, 1, 5356, 105, 1, 1, 5886, 110

Offset: 1

Author

Felix Huber, Apr 04 2025

Keywords

• nonn

Comments

a(n) is the number of positive integers k for which A007947(A071174(k)) = A144338(n).

Examples

			The a(6) = 9 numbers in A071174 that have the radical A144338(6) = 10 are 2^9*5^1 = 2560, 2^8*5^2 = 6400, 2^7*5^3 = 16000, 2^6*5^4 = 40000, 2^5*5^5 = 100000, 2^4*5^6 = 250000, 2^3*5^7 = 625000, 2^2*5^8 = 1562500, 2^1*5^9 = 3906250.
		

Links

• Felix Huber, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007947, A071174, A144338.

Programs

Maple

A144338:=proc(n)
    option remember;
    local a;
    if n=1 then
        2
    else
        for a from procname(n-1)+1 do
            if IsSquareFree(a) then
                return a
            fi
        od
    fi;
end proc;
A382408:=n->binomial(A144338(n)-1,A144338(n)-NumberTheory:-Omega(A144338(n)));
seq(A382408(n),n=1..69);

Formula

a(n) = binomial(A144338(n) - 1, A144338(n) - Omega(A144338(n))).