OFFSET
1,2
COMMENTS
The Heinz number of a partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). This gives a bijective correspondence between positive integers and integer partitions.
EXAMPLE
The terms and their prime indices begin:
1: {}
3: {2}
6: {1,2}
9: {2,2}
10: {1,3}
18: {1,2,2}
20: {1,1,3}
36: {1,1,2,2}
40: {1,1,1,3}
54: {1,2,2,2}
56: {1,1,1,4}
60: {1,1,2,3}
108: {1,1,2,2,2}
112: {1,1,1,1,4}
120: {1,1,1,2,3}
216: {1,1,1,2,2,2}
224: {1,1,1,1,1,4}
240: {1,1,1,1,2,3}
MATHEMATICA
Select[Range[1000], Floor[2*Total[Cases[FactorInteger[#], {p_, k_}:>k*PrimePi[p]]]/3]==PrimeOmega[#]&]
PROG
(PARI)
A056239(n) = { my(f); if(1==n, 0, f=factor(n); sum(i=1, #f~, f[i, 2] * primepi(f[i, 1]))); }
isA348550(n) = (bigomega(n)==floor((2/3)*A056239(n))); \\ Antti Karttunen, Nov 08 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 05 2021
STATUS
approved