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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 Antti Karttunen, Table of n, a(n) for n = 1..10000 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 Cf. A000005, A000203, A001710, A064945, A064944, A130674. Sequence in context: A140145 A166643 A038302 * A188001 A273614 A281224 Adjacent sequences: A246913 A246914 A246915 * A246917 A246918 A246919 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.)