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
Keywords
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
Programs
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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:
Comments