A097974 -id:A097974 - cp's OEIS frontend

A347160 Sum of 4th powers of distinct prime divisors of n that are <= sqrt(n).

0, 0, 0, 16, 0, 16, 0, 16, 81, 16, 0, 97, 0, 16, 81, 16, 0, 97, 0, 16, 81, 16, 0, 97, 625, 16, 81, 16, 0, 722, 0, 16, 81, 16, 625, 97, 0, 16, 81, 641, 0, 97, 0, 16, 706, 16, 0, 97, 2401, 641, 81, 16, 0, 97, 625, 2417, 81, 16, 0, 722, 0, 16, 2482, 16, 625, 97, 0, 16, 81, 3042

Offset: 1

Ilya Gutkovskiy, Aug 20 2021

nonn

Cf. A001159, A005065, A005068, A063962, A097974, A098002, A347143, A347158, A347159.

Table[DivisorSum[n, #^4 &, # <= Sqrt[n] && PrimeQ[#] &], {n, 1, 70}]
nmax = 70; CoefficientList[Series[Sum[Prime[k]^4 x^(Prime[k]^2)/(1 - x^Prime[k]), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

G.f.: Sum_{k>=1} prime(k)^4 * x^(prime(k)^2) / (1 - x^prime(k)).

A382486 Product of distinct prime divisors of n that are <= sqrt(n).

Original entry on oeis.org

1, 1, 1, 2, 1, 2, 1, 2, 3, 2, 1, 6, 1, 2, 3, 2, 1, 6, 1, 2, 3, 2, 1, 6, 5, 2, 3, 2, 1, 30, 1, 2, 3, 2, 5, 6, 1, 2, 3, 10, 1, 6, 1, 2, 15, 2, 1, 6, 7, 10, 3, 2, 1, 6, 5, 14, 3, 2, 1, 30, 1, 2, 21, 2, 5, 6, 1, 2, 3, 70, 1, 6, 1, 2, 15, 2, 7, 6, 1, 10, 3, 2, 1, 42, 5

Offset: 1

Ilya Gutkovskiy, Apr 10 2025

nonn

Cf. A007947, A007955, A072499, A097974.

Table[Times @@ Select[Divisors[n], PrimeQ[#] && # <= Sqrt[n] &], {n, 1, 85}]

a(n) = vecprod(select(x->x<=sqrt(n), factor(n)[,1])); \\ Michel Marcus, Apr 17 2025

a(p) = 1, for prime p.

cp's OEIS Frontend

A347160 Sum of 4th powers of distinct prime divisors of n that are <= sqrt(n).

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