A190403 Number n for which sigma(n)=sigma(n'), where sigma is the sum of divisors and n' the arithmetic derivative of n.

4, 27, 60, 84, 132, 140, 204, 220, 228, 260, 270, 340, 372, 378, 444, 492, 564, 572, 580, 620, 644, 702, 708, 740, 804, 812, 820, 836, 860, 884, 918, 945, 1026, 1068, 1180, 1242, 1276, 1284, 1292, 1308, 1316, 1364, 1420, 1460, 1484, 1485, 1508, 1564, 1566

Offset

1,1

Links

Nathaniel Johnston, Table of n, a(n) for n = 1..10000

Maple

with(numtheory);
P:=proc(i)
local f, n, p, pfs;
for n from 1 to i do
    pfs:=ifactors(n)[2];
    f:=n*add(op(2, p)/op(1, p), p=pfs);
    if sigma(n)=sigma(f) then print(n); fi;
od;
end:
P(1000);

Mathematica

d[0] = d[1] = 0; d[n_] := n*Total[f = FactorInteger[n]; f[[All, 2]]/f[[All, 1]] ]; Reap[For[n = 1, n < 2000, n++, If[DivisorSigma[1, n] == DivisorSigma[1, d[n]], Sow[n]]]][[2, 1]] (* Jean-François Alcover, Apr 22 2015 *)

Prog

(Python)
from sympy import factorint, totient
A190402 = [n for n in range(2, 10**3) if totient(int(sum([n*e/p for p, e in factorint(n).items()]))) == totient(n)] # Chai Wah Wu, Aug 21 2014

Crossrefs

Cf. A000203, A003415, A189057, A190402.

Sequence in context: A347671 A033663 A218629 * A141091 A349200 A078111

Adjacent sequences: A190400 A190401 A190402 * A190404 A190405 A190406

Keyword

nonn,easy

Author

Paolo P. Lava, May 10 2011

Status

approved