A136183 - OEIS

A136183

a(n) = Sum_{k=1..d(n)-1} lcm(b(k), b(k+1)), where b(k) is the k-th positive divisor of n and d(n) = number of positive divisors of n.

0, 2, 3, 6, 5, 14, 7, 14, 12, 22, 11, 44, 13, 30, 33, 30, 17, 50, 19, 56, 45, 46, 23, 104, 30, 54, 39, 76, 29, 143, 31, 62, 69, 70, 75, 158, 37, 78, 81, 166, 41, 154, 43, 116, 153, 94, 47, 224, 56, 122, 105, 136, 53, 158, 115, 230, 117, 118, 59, 400, 61, 126, 213, 126, 135

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OFFSET

1,2

COMMENTS

a(n) = sum of the terms in row n of A136181.

LINKS

H. v. Eitzen, Table of n, a(n) for n=1..10000

Index entries for sequences related to lcm's

EXAMPLE

The positive divisors of 20 are 1,2,4,5,10,20; lcm(1,2)=2, lcm(2,4)=4, lcm(4,5)=20, lcm(5,10)=10, and lcm(10,20)=20, so a(20) = 2+4+20+10+20 = 56.

MAPLE

A136181row := proc(n) local dvs; dvs := sort(convert(numtheory[divisors](n), list)) ; seq(lcm(op(d-1, dvs), op(d, dvs)), d=2..nops(dvs)) ; end: A136183 := proc(n) if n = 1 then 0; else add(l, l= A136181row(n) ) ; fi; end: seq(A136183 (n), n=1..70) ; # R. J. Mathar, Jul 20 2009

MATHEMATICA

Table[Total@ Apply[LCM, Partition[Divisors@ n, 2, 1], 1], {n, 65}] (* Michael De Vlieger, Sep 21 2017 *)

PROG

(PARI) A136183(n) = local(d=divisors(n)); vector(#d-1, x, lcm(d[x], d[x+1]))*vector(#d-1, x, 1)~

(PARI) a(n) = my(d=divisors(n)); vecsum(vector(#d-1, k, lcm(d[k], d[k+1]))); \\ Michel Marcus, Sep 22 2017

(Haskell)

a136183 n = sum $ zipWith lcm ps $ tail ps where ps = a027750_row n

-- Reinhard Zumkeller, Dec 20 2014

CROSSREFS

Cf. A136180, A136181, A136182.

Cf. A027750.

Sequence in context: A053570 A129647 A225652 * A100211 A382221 A071257