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A358105
Unreduced denominator of the n-th divisible pair, where pairs are ordered by Heinz number. Lesser prime index of A318990(n).
6
1, 1, 2, 1, 1, 2, 1, 3, 1, 1, 1, 2, 1, 4, 2, 1, 1, 3, 1, 1, 1, 2, 1, 1, 2, 3, 1, 5, 1, 2, 4, 1, 1, 1, 1, 2, 1, 6, 1, 2, 3, 1, 1, 1, 2, 1, 1, 1, 3, 2, 1, 4, 1, 2, 1, 1, 7, 1, 1, 2, 3, 1, 5, 2, 1, 1, 2, 1, 1, 8, 1, 3, 4, 1, 1, 2, 1, 1, 2, 1, 3, 1, 2, 1, 1, 1, 1
OFFSET
1,3
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.
FORMULA
A358103(n) = A358104(n)/a(n).
EXAMPLE
The 12th divisible pair is (2,6) so a(12) = 2.
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]:>x, {0}], {n, 1000}]
CROSSREFS
The divisible pairs are ranked by A318990, proper A339005.
For all semiprimes we have A338912, greater A338913.
The quotient of the pair is A358103.
The reduced version for all semiprimes is A358193, numerator A358192.
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.
Sequence in context: A346175 A165357 A346741 * A210961 A250007 A048996
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 02 2022
STATUS
approved