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A367590
Numbers with exactly two distinct prime factors, both appearing with the same exponent.
3
6, 10, 14, 15, 21, 22, 26, 33, 34, 35, 36, 38, 39, 46, 51, 55, 57, 58, 62, 65, 69, 74, 77, 82, 85, 86, 87, 91, 93, 94, 95, 100, 106, 111, 115, 118, 119, 122, 123, 129, 133, 134, 141, 142, 143, 145, 146, 155, 158, 159, 161, 166, 177, 178, 183, 185, 187, 194
OFFSET
1,1
COMMENTS
First differs from A268390 in lacking 210.
First differs from A238748 in lacking 210.
These are the Heinz numbers of the partitions counted by A367588.
LINKS
FORMULA
Union of A006881 and A303661. - Michael De Vlieger, Dec 01 2023
EXAMPLE
The terms together with their prime indices begin:
6: {1,2} 57: {2,8} 106: {1,16}
10: {1,3} 58: {1,10} 111: {2,12}
14: {1,4} 62: {1,11} 115: {3,9}
15: {2,3} 65: {3,6} 118: {1,17}
21: {2,4} 69: {2,9} 119: {4,7}
22: {1,5} 74: {1,12} 122: {1,18}
26: {1,6} 77: {4,5} 123: {2,13}
33: {2,5} 82: {1,13} 129: {2,14}
34: {1,7} 85: {3,7} 133: {4,8}
35: {3,4} 86: {1,14} 134: {1,19}
36: {1,1,2,2} 87: {2,10} 141: {2,15}
38: {1,8} 91: {4,6} 142: {1,20}
39: {2,6} 93: {2,11} 143: {5,6}
46: {1,9} 94: {1,15} 145: {3,10}
51: {2,7} 95: {3,8} 146: {1,21}
55: {3,5} 100: {1,1,3,3} 155: {3,11}
MATHEMATICA
Select[Range[100], SameQ@@Last/@If[#==1, {}, FactorInteger[#]]&&PrimeNu[#]==2&]
CROSSREFS
The case of any multiplicities is A007774, counts A002133.
Partitions of this type are counted by A367588.
The case of distinct exponents is A367589, counts A182473.
A000041 counts integer partitions, strict A000009.
A091602 counts partitions by greatest multiplicity, least A243978.
A116608 counts partitions by number of distinct parts.
Sequence in context: A362617 A374472 A238748 * A268390 A265693 A211484
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 01 2023
STATUS
approved