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A330503 Number of Sós permutations of {0,1,...,n}. 1
2, 6, 16, 30, 60, 84, 144, 198, 280, 352, 504, 598, 812, 960, 1152, 1360, 1728, 1938, 2400, 2688, 3080, 3450, 4128, 4500, 5200, 5724, 6440, 7018, 8100, 8618, 9856, 10692, 11696, 12600, 13824, 14652, 16416, 17550, 18960, 20090, 22260, 23306, 25696, 27180, 28888 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..45.

S. Bockting-Conrad, Y. Kashina, T. K. Petersen, and B. E. Tenner, Sós permutations, arXiv:2007.01132 [math.CO], 2020.

FORMULA

a(n) = (n+1) * Sum_{k=1..n} phi(k), where phi(k) is Euler's totient function.

a(n) = (n+1) * A002088(n).

EXAMPLE

For n = 3, the a(3) = 16 Farey functions of {0,1,2,3} are {0123, 3012, 2301, 1230, 0312, 2031, 1203, 3120, 0213, 3021, 1302, 2130, 0321, 1032, 2103, 3210}.

MATHEMATICA

MapIndexed[(First[#2] + 1) #1 &, Accumulate@ Array[EulerPhi, 45]] (* Michael De Vlieger, Dec 16 2019 *)

PROG

(PARI) a(n)={(n+1)*sum(k=1, n, eulerphi(k))} \\ Andrew Howroyd, Dec 20 2019

(Python)

from functools import lru_cache

@lru_cache(maxsize=None)

def A330503(n):

    if n == 0:

        return 0

    c, j = 0, 2

    k1 = n//j

    while k1 > 1:

        j2 = n//k1 + 1

        c += (j2-j)*(2*A330503(k1)//(k1+1)-1)

        j, k1 = j2, n//j2

    return (n+1)*(n*(n-1)-c+j)//2 # Chai Wah Wu, Mar 29 2021

CROSSREFS

Cf. A002088.

Sequence in context: A160620 A005996 A192735 * A171218 A032091 A182994

Adjacent sequences:  A330500 A330501 A330502 * A330504 A330505 A330506

KEYWORD

easy,nonn

AUTHOR

Bridget Tenner, Dec 16 2019

EXTENSIONS

More terms from Michael De Vlieger, Dec 16 2019

STATUS

approved

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Last modified July 27 16:52 EDT 2021. Contains 346308 sequences. (Running on oeis4.)