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

Author

Paolo P. Lava, Sep 25 2013

Keywords

• nonn
• more

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

Examples

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

Crossrefs

Cf. A003415, A227848.

Programs

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);

PARI

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

Formula

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