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

1,4

Comments

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

Links

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

Formula

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

Example

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.

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);

Crossrefs

Cf. A007947, A071174, A144338.

Sequence in context: A193856 A255294 A115521 * A140705 A336053 A266072

Adjacent sequences: A382405 A382406 A382407 * A382409 A382410 A382411

Keyword

nonn

Author

Felix Huber, Apr 04 2025

Status

approved