A229501 Numbers k such that Sum_{i=1..k} i' == 0 (mod k), where i' is the arithmetic derivative of i.

1, 6, 344, 1475, 3816, 5463, 18468, 78894, 515108, 566932, 1600370, 14380856, 27129564, 28669993, 31401775, 39638108, 2245196680, 2878016306, 5890364987, 7838325300, 23168759538, 63226475740, 121869542099

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,more

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