OFFSET
1,1
COMMENTS
A mode in a multiset is an element that appears at least as many times as each of the others. For example, the modes of {a,a,b,b,b,c,d,d,d} are {b,d}.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
The prime indices of 180 are {1,1,2,2,3}, with modes {1,2}, so 180 is in the sequence, and the sequence differs from A182853.
The terms together with their prime indices begin:
6: {1,2}
10: {1,3}
14: {1,4}
15: {2,3}
21: {2,4}
22: {1,5}
26: {1,6}
30: {1,2,3}
33: {2,5}
34: {1,7}
35: {3,4}
36: {1,1,2,2}
38: {1,8}
39: {2,6}
42: {1,2,4}
46: {1,9}
51: {2,7}
55: {3,5}
MAPLE
q:= n-> (l-> nops(l)>1 and l[-1]=l[-2])(sort(map(i-> i[2], ifactors(n)[2]))):
select(q, [$1..250])[]; # Alois P. Heinz, May 10 2023
MATHEMATICA
Select[Range[100], Count[Last/@FactorInteger[#], Max@@Last/@FactorInteger[#]]>1&]
PROG
(Python)
from sympy import factorint
def ok(n): return n>1 and (e:=list(factorint(n).values())).count(max(e))>1
print([k for k in range(155) if ok(k)]) # Michael S. Branicky, May 06 2023
(PARI) is(n) = {my(e = factor(n)[, 2]); if(#e < 2, 0, e = vecsort(e); e[#e-1] == e[#e]); } \\ Amiram Eldar, Jan 20 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 05 2023
STATUS
approved