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A307327 Number of superabundant m in the interval p_k# <= m < p_(k+1)#, where p_i# = A002110(i). 1
1, 2, 3, 5, 6, 6, 5, 9, 8, 9, 8, 11, 12, 11, 11, 10, 12, 12, 11, 14, 15, 15, 16, 12, 14, 14, 15, 12, 12, 12, 12, 14, 13, 14, 12, 12, 14, 15, 16, 15, 15, 16, 18, 15, 17, 18, 18, 21, 22, 17, 15, 19, 17, 15, 16, 17, 16, 16, 17, 18, 18, 17, 17, 16, 17, 15, 15, 14 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Also first differences of the number of terms m in A004394 such that m < A002110(k).

Analogous to A307113.

Terms m in A004394 (superabundant numbers) are products of primorials.

The primorial A002110(k) is the smallest number that is the product of the k smallest primes.

This sequence partitions A004394 using terms in A002110.

First terms {1, 2, 3, 5, 6} are the same as those of A307113, since the first 19 terms of A002182 and A004394 are identical.

LINKS

Michael De Vlieger, Table of n, a(n) for n = 0..407

Michael De Vlieger, Graph comparing a(n) in red with A307113(n) in blue

EXAMPLE

First terms of this sequence and the superabundant numbers within the intervals:

n  a(n)      m such that A002110(n) <= m < A002110(n+1)

-------------------------------------------------------

0    1       1*

1    2       2*      4

2    3       6*     12      24

3    5      36      48      60     120     180

4    6     240     360     720     840    1260    1680

5    6    2520    5040   10080   15120   25200   27720

6    5   55440  110880  166320  277200  332640

...

(Asterisks denote primorials in A004394.)

MATHEMATICA

Block[{nn = 8, P, s}, P = Nest[Append[#, #[[-1]] Prime@ Length@ #] &, {1}, nn + 1]; s = Array[DivisorSigma[1, # ]/# &, P[[nn + 1]]];  s = Map[FirstPosition[s, #][[1]] &, Union@ FoldList[Max, s]]; Table[Count[s, _?(If[! IntegerQ@ #, 1, #] &@ P[[i]] <= # < P[[i + 1]] &)], {i, nn}]]

CROSSREFS

Cf. A002110, A002182, A004394, A307113.

Sequence in context: A001600 A175578 A316609 * A000036 A165081 A165089

Adjacent sequences:  A307324 A307325 A307326 * A307328 A307329 A307330

KEYWORD

nonn

AUTHOR

Michael De Vlieger, Apr 02 2019

STATUS

approved

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Last modified January 24 07:18 EST 2020. Contains 331189 sequences. (Running on oeis4.)