A349543 a(n) = A001414(A277272(n)).

2, 4, 6, 3, 6, 9, 9, 9, 15, 5, 5, 10, 8, 8, 8, 10, 10, 10, 14, 7, 7, 7, 21, 9, 12, 10, 16, 12, 15, 25, 20, 14, 12, 16, 22, 11, 11, 11, 11, 11, 11, 33, 12, 12, 18, 16, 26, 13, 13, 13, 13, 39, 21, 14, 12, 18, 18, 12, 14, 22, 32, 20, 45, 27, 24, 34, 17, 17, 17, 17

Offset: 1

Author

Michael De Vlieger, Nov 21 2021

Keywords

• nonn

Comments

Although terms k in A277272 are distinct, terms m in this sequence may appear A000607(m) times, even consecutively.

The restriction of the number of appearances of m to A000607(m) is a consequence of distinct k such that A001414(k) = m. Distinct k for which A001414(k) = m relates to the number of prime partitions of m and are listed in row m of A064364. For example, k in {7, 10, 12} have A001414(k) = 7. Once these k have appeared in A277272, there is no other way to obtain m = 7 in this sequence. Hence m = 7 is exhausted in this sequence.

Terms are greater than 1.

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10001
• Michael De Vlieger, Log log scatterplot of a(n) for n=1..2^17, accentuating n <= 2^10 with small points, and n <= 32 with medium points for better visibility.

Crossrefs

Cf. A000607, A001414, A064364, A277272.

Programs

Mathematica

m = 2, n = 1, s[] = c[] = 0; s[2] = 2; c[2]++; {2}~Join~Reap[Do[k = 3; While[Nand[GCD[If[s[k] == 0, Set[s[k], Total@ Flatten[ConstantArray[#1, #2] & @@@ FactorInteger[k]]], s[k]], s[m]] > 1, c[k] == 0], k++]; Set[n, k]; Sow[s[k]]; c[n]++; m = n, 70]][[-1, -1]]