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

Author

Rémy Sigrist, Apr 02 2021

Keywords

• nonn

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

Examples

			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.
		

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

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.

Programs

Mathematica

Table[n^2/FactorInteger[n][[-1,1]],{n,100}] (* Gus Wiseman, Aug 09 2021 *)

PARI

See Links section.

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)