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A246916 Sum of the cumulative sums of all the permutations of divisors of number n. 1
1, 9, 12, 84, 18, 720, 24, 900, 156, 1080, 36, 70560, 42, 1440, 1440, 11160, 54, 98280, 60, 105840, 1920, 2160, 72, 10886400, 372, 2520, 2400, 141120, 90, 13063680, 96, 158760, 2880, 3240, 2880, 165110400, 114, 3600, 3360, 16329600, 126, 17418240, 132, 211680 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
For number n there are A130674(n) = tau(n)! = A000005(n)! permutations of divisors of number n and the same number of their cumulative sums. This sequence is sequence of sums of these sums.
Sequences A064945 and A064944 are sequences of minimal and maximal values of cumulative sums of all the permutations of divisors of number n.
LINKS
FORMULA
a(n) = A130674 (n) * ((A064945(n) + A064944(n)) / 2) = (tau(n))! * (((Sum_{i=1..tau(n)} ((tau(n) - i + 1)*d_i) + (Sum_{i=1..tau(n)}( i*d_i))) / 2); where {d_i}, i = 1…tau(n) is increasing sequence of divisors of n.
a(n) = sigma(n) * A001710(tau(n) + 1) = A000203(n) * A001710(A000005(n)+1).
EXAMPLE
For n = 4; there are tau(4)! = 6 permutations of divisors of number 4: (1, 2, 4); (1, 4, 2); (2, 1, 4); (2, 4, 1); (4, 1, 2); (4, 2, 1). Sum of their cumulative sums = 11 + 13 + 12 + 15 + 16 + 17 = 84.
PROG
(Magma) [SumOfDivisors(n)*(Order(AlternatingGroup(NumberOfDivisors(n)+1))): n in [1..100]]
(PARI)
A001710(n) = if( n<2, n>=0, n!/2);
A246916(n) = (sigma(n) * A001710(numdiv(n) + 1)); \\ Antti Karttunen, Sep 10 2017
CROSSREFS
Sequence in context: A140145 A166643 A038302 * A188001 A273614 A281224
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Sep 12 2014
STATUS
approved

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Last modified June 20 18:51 EDT 2024. Contains 373532 sequences. (Running on oeis4.)