OFFSET
1,2
COMMENTS
A number is 5-smooth if its prime divisors are all <= 5.
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.
EXAMPLE
The sequence of terms together with their prime indices begins:
1: {} 125: {3,3,3}
3: {2} 135: {2,2,2,3}
5: {3} 150: {1,2,3,3}
9: {2,2} 225: {2,2,3,3}
10: {1,3} 243: {2,2,2,2,2}
15: {2,3} 250: {1,3,3,3}
25: {3,3} 270: {1,2,2,2,3}
27: {2,2,2} 300: {1,1,2,3,3}
30: {1,2,3} 375: {2,3,3,3}
45: {2,2,3} 405: {2,2,2,2,3}
50: {1,3,3} 450: {1,2,2,3,3}
75: {2,3,3} 500: {1,1,3,3,3}
81: {2,2,2,2} 625: {3,3,3,3}
90: {1,2,2,3} 675: {2,2,2,3,3}
100: {1,1,3,3} 729: {2,2,2,2,2,2}
MATHEMATICA
Select[Range[1000], PrimeOmega[#]<=Total[Cases[FactorInteger[#], {p_, k_}:>k*PrimePi[p]]]/2&&Max@@First/@FactorInteger[#]<=5&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 16 2021
STATUS
approved