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A190403 Number n for which sigma(n)=sigma(n'), where sigma is the sum of divisors and n' the arithmetic derivative of n. 4
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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: A051506 A033663 A218629 * A141091 A078111 A186882

Adjacent sequences:  A190400 A190401 A190402 * A190404 A190405 A190406

KEYWORD

nonn,easy

AUTHOR

Paolo P. Lava, May 10 2011

STATUS

approved

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Last modified October 13 22:30 EDT 2019. Contains 327983 sequences. (Running on oeis4.)