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

Author

Michel Lagneau, Dec 13 2013

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

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

Crossrefs

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

Programs

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: