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A163180 a(n) = tau(n) + Sum_{k=1..n} (n mod k). 2
1, 2, 3, 4, 6, 7, 10, 12, 15, 17, 24, 23, 30, 35, 40, 41, 53, 53, 66, 67, 74, 81, 100, 93, 106, 116, 129, 130, 153, 146, 169, 173, 188, 201, 222, 207, 235, 252, 273, 266, 299, 292, 327, 334, 345, 362, 405, 384, 417, 426, 453, 460, 507, 500, 533, 528, 557, 582, 637, 598, 647 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Number of divisors of n plus the sum of all the remainders modulo the numbers below n.

LINKS

Table of n, a(n) for n=1..61.

FORMULA

a(n) = A000005(n) + A004125(n).

EXAMPLE

a(1) = 1 + 0 = 1;

a(2) = 2 + 0 = 2;

a(3) = 2 + 1 = 3;

a(4) = 3 + 1 = 4;

a(5) = 2 + 4 = 6.

MAPLE

A004125 := proc(n) add( modp(n, k), k=2..n) ; end: A163180 := proc(n) numtheory[tau](n)+A004125(n) ; end: seq(A163180(n), n=1..80) ; # R. J. Mathar, Jul 27 2009

MATHEMATICA

Table[DivisorSigma[0, n]+Sum[Mod[n, k], {k, n}], {n, 70}] (* Harvey P. Dale, Feb 11 2015 *)

CROSSREFS

Cf. A000005, A004125.

Sequence in context: A099523 A049806 A158381 * A091515 A036405 A051424

Adjacent sequences:  A163177 A163178 A163179 * A163181 A163182 A163183

KEYWORD

nonn

AUTHOR

Juri-Stepan Gerasimov, Jul 22 2009

EXTENSIONS

169 inserted by R. J. Mathar, Jul 27 2009

STATUS

approved

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Last modified August 14 19:09 EDT 2020. Contains 336483 sequences. (Running on oeis4.)