A064945 - OEIS

A064945

a(n) = Sum_{i|n, j|n, j >= i} i.

1, 4, 5, 11, 7, 22, 9, 26, 18, 30, 13, 64, 15, 38, 38, 57, 19, 82, 21, 87, 48, 54, 25, 156, 38, 62, 58, 109, 31, 179, 33, 120, 68, 78, 68, 244, 39, 86, 78, 213, 43, 224, 45, 153, 143, 102, 49, 348, 66, 166, 98, 175, 55, 268, 96, 267, 108, 126, 61, 542, 63, 134, 181

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

a(n) = a(n+1) for n=14, 14229, 194931, 8897930, 278110142, ... . - Michel Marcus, Jun 10 2015

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = Sum_{i=1..tau(n)} (tau(n)-i+1)*d_i, where {d_i}, i=1..tau(n), is the increasing sequence of divisors of n.

a(n) = Sum_{i=1..A000005(n)} (A000005(n)-i+1)*A027750(n, i). - Michel Marcus, Jun 10 2015

EXAMPLE

a(6) = dot_product(4,3,2,1)*(1,2,3,6) = 4*1+3*2+2*3+1*6 = 22.

MAPLE

with(numtheory): seq(add((tau(n)-i+1)*sort(convert(divisors(n), 'list'))[i], i=1..tau(n)), n=1..200);

PROG

(PARI) { for (n=1, 1000, d=divisors(n); t=length(d); a=sum(i=1, t, (t - i + 1)*d[i]); write("b064945.txt", n, " ", a) ) } \\ Harry J. Smith, Oct 01 2009

(PARI) a(n)=my(d=divisors(n)); sum(i=1, #d, (#d+1-i)*d[i]) \\ Charles R Greathouse IV, Jun 10 2015

(Haskell)

a064945 = sum . zipWith (*) [1..] . reverse . a027750_row'

-- Reinhard Zumkeller, Jul 14 2015

CROSSREFS

Cf. A000005, A000203, A060640, A064944.

Cf. A027750.

Sequence in context: A322655 A206028 A007429 * A069820 A318446 A317304

Adjacent sequences: A064942 A064943 A064944 * A064946 A064947 A064948

KEYWORD

nonn,easy

AUTHOR

Vladeta Jovovic, Oct 28 2001

STATUS

approved