A238905 The tau(sigma)-perfect numbers, where the set of f-perfect numbers for an arithmetical function f is defined in A066218.

6, 15, 22, 33, 39, 57, 69, 111, 129, 141, 183, 201, 214, 219, 237, 309, 453, 471, 489, 573, 579, 633, 669, 813, 831, 849, 939, 993, 1101, 1149, 1191, 1263, 1371, 1389, 1461, 1519, 1569, 1623, 1641, 1821, 1839, 1893, 1942, 1983, 2019, 2073, 2199, 2253, 2271

Offset: 1

Author

Paolo P. Lava, Mar 07 2014

Keywords

• nonn
• easy

Examples

			Aliquot divisors of 39 are 1, 3, 13. Then tau(sigma(1)) + tau(sigma(3)) + tau(sigma(13)) = 1 + 3 + 4 = 8 and tau(sigma(39)) = 8.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Paolo P. Lava)

Crossrefs

Cf. A000005, A000230, A066218.

Programs

Maple

with(numtheory); P:=proc(q) local a,b,i,n;
for n from 1 to q do a:=divisors(n); b:=0;
for i from 1 to nops(a)-1 do b:=b+tau(sigma(a[i])); od;
if tau(sigma(n))=b then print(n); fi; od; end: P(10^6);

Mathematica

q[n_] := DivisorSum[n, DivisorSigma[0, DivisorSigma[1, #]] &, # < n &] == DivisorSigma[0, DivisorSigma[1, n]]; Select[Range[2300], q] (* Amiram Eldar, Aug 22 2023 *)

PARI

isok(n) = numdiv(sigma(n)) == sumdiv(n, d, (dMichel Marcus, Mar 08 2014