

A338900


Difference between the two prime indices of the nth squarefree semiprime.


28



1, 2, 3, 1, 2, 4, 5, 3, 6, 1, 7, 4, 8, 5, 2, 6, 9, 10, 3, 7, 11, 1, 12, 4, 13, 8, 2, 9, 14, 5, 15, 10, 6, 16, 3, 17, 11, 12, 4, 18, 13, 19, 1, 7, 20, 8, 21, 14, 5, 22, 15, 23, 16, 9, 2, 24, 17, 25, 6, 10, 26, 3, 18, 27, 11, 7, 28, 19, 1, 29, 12, 20, 2, 21, 4
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OFFSET

1,2


COMMENTS

A squarefree semiprime is a product of any two distinct prime numbers. A prime index of n is a number m such that the mth prime number divides n. The multiset of prime indices of n is row n of A112798.
Is this sequence an antirun, i.e., are there no adjacent equal parts? I have verified this conjecture up to n = 10^6.  Gus Wiseman, Nov 18 2020


LINKS



FORMULA

If the nth squarefree semiprime is prime(x) * prime(y) with x < y, then a(n) = y  x.


MATHEMATICA

Subtract@@PrimePi/@First/@FactorInteger[#]&/@Select[Range[100], SquareFreeQ[#]&&PrimeOmega[#]==2&]


CROSSREFS

A176506 is the not necessarily squarefree version.
A338899 has rowdifferences equal to this sequence.
A338901 gives positions of first appearances.
A001221 counts distinct prime indices.
A004526 counts 2part partitions, with strict case A140106 (shifted left).
A065516 gives first differences of semiprimes.
A166237 gives first differences of squarefree semiprimes.
Cf. A000040, A056239, A112798, A167171, A320656, A320891, A320894, A320911, A338898, A338905, A338908.


KEYWORD

nonn


AUTHOR



STATUS

approved



