A390516 a(n) is the number of occurrences of n^2 in A390375.

0, 2, 1, 2, 2, 1, 3, 1, 3, 2, 1, 4, 3, 1, 3, 2, 4, 1, 3, 2, 1, 3, 2, 4, 5, 1, 1, 2, 1, 2, 6, 2, 3, 1, 6, 1, 2, 4, 2, 1, 3, 1, 4, 1, 2, 1, 7, 8, 2, 1, 1, 3, 1, 3, 3, 3, 3, 1, 2, 2, 1, 3, 8, 2, 1, 2, 8, 3, 4, 1, 1, 3, 3, 2, 2, 3, 2, 5, 2, 3, 5, 1, 3, 1, 2, 1, 4, 4

Offset

0,2

Links

Felix Huber, Table of n, a(n) for n = 0..10000

Formula

a(n) >= 1 for n >= 1 because A390375(prime(n^2)) = n^2.

a(n) = Sum_{i=1..prime(n+1)-1} [A390375(i) = n^2] + 1 for n >= 2.

Example

a(6) = 3 because 6^2 = 36 appears exactly 3 times in A390375: A390375(14) = A390375(15) = A390375(151) = 36.

Maple

with(numtheory):
A390516list := proc(N) # To get the terms a(0) to a(N)
local a, n, l;
if N = 0 then a := 0 else
    l := [seq(A390375(n), n=1..ithprime(N+1))];
    a := 0, 2;
    for n from 2 to N do
        a := a, numboccur(n^2, l[1..ithprime(n+1)-1]) + 1
    od;
fi; return a; end proc:
A390516list(87);

Crossrefs

Cf. A000040, A000290, A390375.

Sequence in context: A366493 A378776 A352998 * A339351 A284322 A219607

Adjacent sequences: A390513 A390514 A390515 * A390517 A390518 A390519

Keyword

nonn,easy

Author

Felix Huber, Nov 09 2025

Status

approved