A358104 Unreduced numerator of the n-th divisible pair, where pairs are ordered by Heinz number. Greater prime index of A318990(n).

1, 2, 2, 3, 4, 4, 5, 3, 6, 7, 8, 6, 9, 4, 8, 10, 11, 6, 12, 13, 14, 10, 15, 16, 12, 9, 17, 5, 18, 14, 8, 19, 20, 21, 22, 16, 23, 6, 24, 18, 12, 25, 26, 27, 20, 28, 29, 30, 15, 22, 31, 12, 32, 24, 33, 34, 7, 35, 36, 26, 18, 37, 10, 28, 38, 39, 30, 40, 41, 8, 42

Offset

1,2

Comments

The Heinz number of a partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). This gives a bijective correspondence between positive integers and integer partitions.

Links

Table of n, a(n) for n=1..71.

Formula

A358103(n) = a(n)/A358105(n).

Example

The 12th divisible pair is (2,6) so a(12) = 6.

Mathematica

primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Join@@Table[Cases[primeMS[n], {x_, y_}/; Divisible[y, x]:>y, {0}], {n, 1000}]

Crossrefs

The divisible pairs are ranked by A318990, proper A339005.

For all semiprimes we have A338913.

The quotient of the pair is A358103.

The denominator is A358105.

The reduced version for all semiprimes is A358192, denominator A358193.

A000040 lists the primes.

A001222 counts prime indices, distinct A001221.

A001358 lists the semiprimes, squarefree A006881.

A003963 multiplies together prime indices.

A056239 adds up prime indices.

A318991 ranks divisor-chains.

Cf. A000720, A032741, A128301, A215366, A289508, A289509, A296150, A300912, A318992, A358106.

Sequence in context: A141525 A209764 A071475 * A343228 A112778 A080594

Adjacent sequences: A358101 A358102 A358103 * A358105 A358106 A358107

Keyword

nonn

Author

Gus Wiseman, Nov 02 2022

Status

approved