OFFSET
1,1
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.
The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), so these are Heinz numbers of integer partitions whose product of parts is divisible by their sum of parts. The enumeration of these partitions by sum is given by A057568.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
The sequence of terms together with their prime indices begins:
2: {1}
3: {2}
5: {3}
7: {4}
9: {2,2}
11: {5}
13: {6}
17: {7}
19: {8}
23: {9}
29: {10}
30: {1,2,3}
31: {11}
37: {12}
41: {13}
43: {14}
47: {15}
49: {4,4}
53: {16}
59: {17}
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[2, 100], Divisible[Times@@primeMS[#], Plus@@primeMS[#]]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 09 2019
STATUS
approved