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A233563 Numbers for which the number of prime divisors counted with multiplicity and the sum of the distinct prime divisors are both perfect. 1
1104, 1656, 2128, 2484, 3726, 4620, 6930, 7448, 11550, 12285, 12696, 16170, 19044, 20216, 20475, 23568, 25410, 26068, 28566, 28665, 34125, 35352, 47775, 53028, 53235, 54544, 66885, 70756, 71875, 79542, 88725, 91238, 124215, 146004, 190904, 192052, 201180 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers n such that A001222(n) and A008472(n) are in the sequence A000396.

LINKS

Donovan Johnson, Table of n, a(n) for n = 1..1000

EXAMPLE

1104 is in the sequence because bigomega(1104) = 6 and sopf(1104) = 28,

23568 is in the sequence because bigomega(23568) = 6 and sopf(23568) = 496,

389904 is in the sequence because bigomega(389904) = 6 and sopf(389904) = 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 bigomega(n)=lst[p] then jj:=1:else fi:od:if ii=1 and jj=1 then printf(`%d, `, n):else fi:od:

CROSSREFS

Cf. A000396, A081357, A008472, A001222, A233482.

Sequence in context: A060519 A197422 A291134 * A127308 A022055 A008688

Adjacent sequences:  A233560 A233561 A233562 * A233564 A233565 A233566

KEYWORD

nonn

AUTHOR

Michel Lagneau, Dec 13 2013

STATUS

approved

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Last modified November 21 04:47 EST 2019. Contains 329350 sequences. (Running on oeis4.)