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A229501 Numbers n such that sum_{i=1..n} i’ == 0 (mod n), where i' is the arithmetic derivative of i. 2
1, 6, 344, 1475, 3816, 5463, 18468, 78894, 515108, 566932, 1600370, 14380856, 27129564, 28669993, 31401775, 39638108, 2245196680, 2878016306, 5890364987, 7838325300, 23168759538, 63226475740, 121869542099 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Next term > 10^7. - M. F. Hasler, Sep 25 2013

a(21) > 10^10. - Donovan Johnson, Sep 25 2013

a(24) > 10^12. - Giovanni Resta, Mar 13 2014

LINKS

Table of n, a(n) for n=1..23.

FORMULA

A229501 = { n | A190121(n) = 0 (mod n) }. - M. F. Hasler, Sep 25 2013

EXAMPLE

1’ + 2’ + 3’ + 4’ + 5’ + 6’ = 0 + 1 + 1 + 4 + 1 + 5 = 12  and  12 mod 6 = 0.

MAPLE

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

for n from 1 to q do a:=a+n*add(op(2, p)/op(1, p), p=ifactors(n)[2]);

if a mod n=0 then print(n); fi; od; end: P(10^6);

PROG

(PARI) s=0; for(n=1, 1e7, (s+=A003415(n))%n||print1(n", ")) \\ - M. F. Hasler, Sep 25 2013

CROSSREFS

Cf. A003415, A227848.

Sequence in context: A144849 A212490 A047941 * A289738 A211089 A221923

Adjacent sequences:  A229498 A229499 A229500 * A229502 A229503 A229504

KEYWORD

nonn

AUTHOR

Paolo P. Lava, Sep 25 2013

EXTENSIONS

Double-checked below 10^6 and extended up to 10^7 by M. F. Hasler, Sep 25 2013

a(12)-a(20) from Donovan Johnson, Sep 25 2013

a(21)-a(23) from Giovanni Resta, Mar 13 2014

STATUS

approved

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Last modified November 19 11:09 EST 2019. Contains 329319 sequences. (Running on oeis4.)