A342768 a(n) = A342767(n, n).

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

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, PARI program for A342768

Index entries for sequences related to dismal (or lunar) arithmetic

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

Cf. A007947, A087019, A342767.

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).

Cf. A000290, A006530, A033942, A037143, A344653, A345957, A346698, A346700, A346704.

Sequence in context: A363501 A066959 A344368 * A340514 A086471 A328846

Adjacent sequences: A342765 A342766 A342767 * A342769 A342770 A342771

Keyword

nonn

Author

Rémy Sigrist, Apr 02 2021

Status

approved