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

1,1

Links

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

Example

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.

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 *)

Prog

(PARI) isok(n) = numdiv(sigma(n)) == sumdiv(n, d, (d<n)*numdiv(sigma(d))); \\ Michel Marcus, Mar 08 2014

Crossrefs

Cf. A000005, A000230, A066218.

Sequence in context: A100410 A095032 A227610 * A187918 A190747 A227229

Adjacent sequences: A238902 A238903 A238904 * A238906 A238907 A238908

Keyword

nonn,easy

Author

Paolo P. Lava, Mar 07 2014

Status

approved