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A341642 Number of strictly superior prime divisors of n. 26
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1

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

Table of n, a(n) for n=1..87.

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}]

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.

The version for squarefree instead of prime divisors is A341595.

The strictly superior prime divisors themselves are listed by A341643.

The version for prime-power instead of prime divisors is A341644.

A001221 counts prime divisors, with sum A001414.

A140271 selects the smallest strictly superior divisor.

A038548 counts superior (or inferior) divisors.

A056924 counts strictly superior (or strictly inferior) divisors.

A207375 list central divisors.

A341673 lists strictly superior divisors.

- Inferior: A033676, A066839, A069288, A161906, A217581, A333749, A333750.

- Superior: A033677, A051283, A059172, A063538, A063539, A070038, A072500, A116882, A116883, A161908, A341592, A341593, A341675, A341676.

- Strictly Inferior: A060775, A333805, A341596, A341674.

- Strictly Superior: A238535, A341644, A341646.

Cf. A000005, A000203, A001222, A001248, A006530, A020639, A112798.

Sequence in context: A030190 A157658 A296211 * A123506 A051105 A284929

Adjacent sequences:  A341639 A341640 A341641 * A341643 A341644 A341645

KEYWORD

nonn

AUTHOR

Gus Wiseman, Feb 21 2021

STATUS

approved

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Last modified May 9 05:08 EDT 2021. Contains 343688 sequences. (Running on oeis4.)