A233482 Numbers for which the number of divisors and the sum of the distinct prime divisors are both perfect.

575, 2057, 2645, 3179, 4416, 8512, 12275, 33534, 94272, 138431, 203075, 218176, 392747, 715878, 918592, 982157, 991841, 1082176, 1205405, 1244387, 1559616, 1690432, 1966912, 2344079, 2464576, 2982976, 3386176, 3452992, 3625792, 3821632, 3867712, 3900497

Offset

1,1

Comments

Numbers n such that A000005(n) and A008472(n) are in the sequence A000396. See the sequence A081357 for the sublime numbers.

Links

Donovan Johnson, Table of n, a(n) for n = 1..333 (terms < 10^11)

Example

575 is in the sequence because tau(575) = 6 and sopf(575) = 28,
4416 is in the sequence because tau(4416) = 28 and sopf(4416) = 28,
12275 is in the sequence because tau(12275) = 6 and sopf(12275) = 496,
203075 is in the sequence because tau(203075) = 6 and sopf(203075) = 8128.

Maple

with(numtheory): lst:={6, 28, 496, 8128, 33550336, 8589869056, 137438691328, 2305843008139952128, 2658455991569831744654692615953842176, 191561942608236107294793378084303638130997321548169216} :n1:=nops(lst): for n from 1 to 1000000 do :x:=factorset(n):n2:=nops(x): s:=sum('x[i]', 'i'=1..n2):
ii:=0:for m from 1 to n1 do:if s=lst[m] then ii:=1:else fi:od:jj:=0:for p from 1 to n1 do:if tau(n)=lst[p] then jj:=1:else fi:od:if ii=1 and jj=1 then printf(`%d, `, n):else fi:od:

Mathematica

Select[Range[4*10^6], AllTrue[{DivisorSigma[0, #], Total[FactorInteger[#][[All, 1]]]}, PerfectNumberQ]&] (* Harvey P. Dale, Aug 11 2021 *)

Crossrefs

Cf A000005, A000396, A081357, A008472.

Sequence in context: A027456 A158372 A230353 * A027527 A069421 A136111

Adjacent sequences: A233479 A233480 A233481 * A233483 A233484 A233485

Keyword

nonn

Author

Michel Lagneau, Dec 11 2013

Status

approved