A326155 Positive integers whose sum of prime indices is divisible by their product of prime indices.

1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 16, 17, 19, 23, 29, 30, 31, 32, 37, 40, 41, 43, 47, 48, 53, 59, 61, 64, 67, 71, 73, 79, 83, 84, 89, 97, 101, 103, 107, 108, 109, 112, 113, 127, 128, 131, 137, 139, 144, 149, 151, 157, 163, 167, 173, 179, 181, 191, 192, 193

Offset

1,2

Comments

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

Also Heinz numbers of the integer partitions counted by A057567. The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

The sequence of terms together with their prime indices begins:
   1: {}
   2: {1}
   3: {2}
   4: {1,1}
   5: {3}
   7: {4}
   8: {1,1,1}
   9: {2,2}
  11: {5}
  12: {1,1,2}
  13: {6}
  16: {1,1,1,1}
  17: {7}
  19: {8}
  23: {9}
  29: {10}
  30: {1,2,3}
  31: {11}
  32: {1,1,1,1,1}
  37: {12}

Mathematica

primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], Divisible[Plus@@primeMS[#], Times@@primeMS[#]]&]

Crossrefs

One and positions of ones in A326153.

Cf. A003963, A056239, A057567, A057568, A112798, A301987.

Cf. A325037, A325042, A325044, A326150, A326151, A326154, A326156, A326158.

Sequence in context: A353844 A353833 A219301 * A079734 A050730 A288221

Adjacent sequences: A326152 A326153 A326154 * A326156 A326157 A326158

Keyword

nonn

Author

Gus Wiseman, Jun 10 2019

Status

approved