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A233482 Numbers for which the number of divisors and the sum of the distinct prime divisors are both perfect. 2
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 (list; graph; refs; listen; history; text; internal format)
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:

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

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Last modified January 22 22:16 EST 2020. Contains 331166 sequences. (Running on oeis4.)