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
Links
- Nathaniel Johnston, Table of n, a(n) for n = 1..10000
Programs
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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 *)
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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