A341642 - OEIS

A341642

Number of strictly superior prime divisors of n.

0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1

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OFFSET

COMMENTS

We define a divisor d|n to be strictly superior if d > n/d. Strictly superior divisors are counted by A056924 and listed by A341673.

All terms are binary numbers.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

EXAMPLE

The sequence of sets of strictly superior prime divisors of each positive integer begins: {}, {2}, {3}, {}, {5}, {3}, {7}, {}, {}, {5}, {11}, {}, {13}, {7}, {5}, {}, {17}, {}, {19}, {5}, ...

MATHEMATICA

Table[Length[Select[Divisors[n], PrimeQ[#]&&#>n/#&]], {n, 100}]

a[n_] := Count[FactorInteger[n][[;; , 1]], _?(#^2 > n &)]; a[1] = 0; Array[a, 100] (* Amiram Eldar, Nov 01 2024 *)

PROG

(PARI) a(n) = #select(x -> (x^2 > n), factor(n)[, 1]); \\ Amiram Eldar, Nov 01 2024

CROSSREFS

Positions of zeros are A048098.

The inferior version is A063962.

Positions of ones are A064052.

The strictly inferior version is A333806.

Dominated by A341591 (the weak version).

The version for odd instead of prime divisors is A341594.