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A050226 Numbers n such that n divides Sum_{k = 1..n} A000005(k). 17
1, 4, 5, 15, 42, 44, 47, 121, 336, 340, 347, 930, 2548, 6937, 6947, 51322, 379097, 379131, 379133, 2801205, 20698345, 56264090, 56264197, 152941920, 152942012, 8350344420, 61701166395, 455913379395, 455913379831, 1239301050694, 3368769533660, 3368769533812 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

Julian Havil, "Gamma: Exploring Euler's Constant", Princeton University Press, Princeton and Oxford, pp. 112-113, 2003.

LINKS

Donovan Johnson, Table of n, a(n) for n = 1..39 (quotients <= 40)

FORMULA

n is in the sequence if Sum_{i = 1..n} d(i) = n*k, k an integer, where d(n) = number of divisors of n.

EXAMPLE

For n = 15 the sum is 1 + 2 + 2 + 3 + 2 + 4 + 2 + 4 + 3 + 4 + 2 + 6 + 2 + 4 + 4 = 45 which is divisible by 15.

MAPLE

with(numtheory); ListA050226:=proc(q) local a, n;  a:=0;

for n from 1 to q do  a:=a+tau(n); if (a mod n)=0 then print(n); fi;

od; end: ListA050226(10^9); # Paolo P. Lava, Jun 28 2013

MATHEMATICA

s = 0; Do[ s = s + DivisorSigma[ 0, n ]; If[ Mod[ s, n ] == 0, Print[ n ] ], {n, 1, 2*10^9} ]

k=10^6; a[1]=1; a[n_]:=a[n]=DivisorSigma[0, n]+a[n-1]; nd=a/@Range@k; Select[Range@k, Divisible[nd[[#]], #]&] (* Ivan N. Ianakiev, Apr 30 2016 *)

PROG

(PARI) lista(nn) = {my(s = 0); for (n=1, nn, s += numdiv(n); if (!(s % n), print1(n, ", ")); ); } \\ Michel Marcus, Dec 14 2015

(Sage)

def A050226_list(len):

    a, L = 0, []

    for n in (1..len):

        a += sigma(n, 0)

        if n.divides(a): L.append(n)

    return L

A050226_list(10000) # Peter Luschny, Dec 18 2015

CROSSREFS

Cf. A000005, A006218, A057494, A085567, A085829.

Sequence in context: A321174 A304921 A051721 * A119562 A289021 A323627

Adjacent sequences:  A050223 A050224 A050225 * A050227 A050228 A050229

KEYWORD

nonn,nice

AUTHOR

Labos Elemer, Dec 20 1999

EXTENSIONS

More terms from Robert G. Wilson v, Sep 21 2000

Further terms from Naohiro Nomoto, Aug 03 2001

a(26)-a(30) from Donovan Johnson, Dec 21 2008

STATUS

approved

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Last modified June 17 17:05 EDT 2019. Contains 324196 sequences. (Running on oeis4.)