A351119 Numbers that are the sum of two balanced numbers in at least one way.

2, 3, 4, 5, 6, 7, 8, 9, 12, 13, 14, 15, 16, 17, 18, 20, 21, 24, 26, 27, 28, 29, 30, 31, 32, 33, 36, 37, 38, 41, 42, 43, 44, 45, 47, 48, 49, 50, 54, 56, 57, 58, 59, 60, 62, 65, 68, 70, 71, 72, 73, 76, 77, 79, 80, 81, 82, 84, 85, 86, 90, 91, 92, 93, 98, 100, 105, 106, 107, 108

Offset

1,1

Comments

A balanced number k is a number such that phi(k) | sigma(k).

Links

Table of n, a(n) for n=1..70.

Example

8 is in the sequence since the balanced numbers less than 8 are: 1, 2, 3, 6 and 6 + 2 = 8.
10 is not in the sequence since the balanced numbers less than 10 are: 1, 2, 3, 6, and no two sum to 10.

Mathematica

m = 100; balanced = Select[Range[m], Divisible[DivisorSigma[1, #], EulerPhi[#]] &]; q[n_] := Length[IntegerPartitions[n, {2}, balanced]] > 0; Select[Range[m], q] (* Amiram Eldar, Feb 01 2022 *)

Prog

(PARI) isb(n) = (sigma(n) % eulerphi(n)) == 0;
isok(m) = for (k=1, m-1, if (isb(k) && isb(m-k), return(1))); \\ Michel Marcus, Feb 01 2022

Crossrefs

Cf. A020492 (balanced numbers).

Sequence in context: A009993 A190218 A055569 * A277046 A305462 A072618

Adjacent sequences: A351116 A351117 A351118 * A351120 A351121 A351122

Keyword

nonn

Author

Wesley Ivan Hurt, Feb 01 2022

Status

approved