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A064605 Partial sum of Sigma_2(n) is divisible by n, where Sigma_2(n)=A001157(n). 8
1, 2, 8, 74, 146, 150, 158, 307, 526, 541, 16157, 20289, 271343, 953614, 1002122, 2233204, 3015123, 15988923, 48033767 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Analogous sequences for various arithmetical functions are A050226, A056650, A064605, A064606, A064607, A064610, A064611, A048290, A062982, A045345.

a(20) > 3*10^10. - Donovan Johnson, Aug 31 2012

LINKS

Table of n, a(n) for n=1..19.

FORMULA

Mod[Sum{sigma_2(j), j=1..n}, n]=Mod[A064602(n), n]=0

EXAMPLE

Summarizing divisor-square sums for j=1,...,8 gives 1+5+10+21+26+50+50+85=248, which is divisible by n=8, so 8 is here and the integer quotient is 31.

MATHEMATICA

k = 1; lst = {}; s = 0; While[k < 1000000001, s = s + DivisorSigma[2, k]; If[ Mod[s, k] == 0, AppendTo[lst, k]; Print@ k]; k++]; lst (* Robert G. Wilson v, Apr 25 2011 *)

CROSSREFS

Cf. A001157, A064602, A050226, A056650, A064606, A064607, A064610, A064611, A064612, A048290, A062982, A045345.

Sequence in context: A013002 A012998 A143760 * A295373 A132039 A204552

Adjacent sequences:  A064602 A064603 A064604 * A064606 A064607 A064608

KEYWORD

nonn

AUTHOR

Labos Elemer, Sep 24 2001

EXTENSIONS

a(15)-a(19) from Donovan Johnson, Jun 21 2010

STATUS

approved

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Last modified January 18 01:10 EST 2022. Contains 350410 sequences. (Running on oeis4.)