A233563 Numbers for which the number of prime divisors counted with multiplicity and the sum of the distinct prime divisors are both perfect.

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

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