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A342768
a(n) = A342767(n, n).
7
1, 2, 3, 8, 5, 12, 7, 32, 27, 20, 11, 48, 13, 28, 45, 128, 17, 108, 19, 80, 63, 44, 23, 192, 125, 52, 243, 112, 29, 180, 31, 512, 99, 68, 175, 432, 37, 76, 117, 320, 41, 252, 43, 176, 405, 92, 47, 768, 343, 500, 153, 208, 53, 972, 275, 448, 171, 116, 59, 720
OFFSET
1,2
COMMENTS
This sequence has similarities with A087019.
These are the positions of first appearances of each positive integer in A346701, and also in A346703. - Gus Wiseman, Aug 09 2021
FORMULA
a(n) = n iff n = 1 or n is a prime number.
a(p^k) = p^(2*k-1) for any k > 0 and any prime number p.
A007947(a(n)) = A007947(n).
A001222(a(n)) = 2*A001222(n) - 1 for any n > 1.
From Gus Wiseman, Aug 09 2021: (Start)
A001221(a(n)) = A001221(n).
If g = A006530(n) is the greatest prime factor of n, then a(n) = n^2/g.
a(n) = A129597(n)/2.
(End)
EXAMPLE
For n = 42:
- 42 = 2 * 3 * 7, so:
2 3 7
x 2 3 7
-------
2 3 7
2 3 3
+ 2 2 2
-----------
2 2 3 3 7
- hence a(42) = 2 * 2 * 3 * 3 * 7 = 252.
MATHEMATICA
Table[n^2/FactorInteger[n][[-1, 1]], {n, 100}] (* Gus Wiseman, Aug 09 2021 *)
PROG
(PARI) See Links section.
CROSSREFS
The sum of prime indices of a(n) is 2*A056239(n) - A061395(n).
The version for even indices is A129597(n) = 2*a(n) for n > 1.
The sorted version is A346635.
These are the positions of first appearances in A346701 and in A346703.
A001221 counts distinct prime factors.
A001222 counts prime factors with multiplicity.
A027193 counts partitions of odd length, ranked by A026424.
A209281 adds up the odd bisection of standard compositions (even: A346633).
A346697 adds up the odd bisection of prime indices (reverse: A346699).
Sequence in context: A363501 A066959 A344368 * A340514 A086471 A328846
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Apr 02 2021
STATUS
approved