The nature of the code given in the following examples is explained in the index document.
Integer sequences which are calculated directly from their indexes
can have another calculation applied to them.
The calculations given below explore such combinations.
Base Functions
Functions to be used as a basis for the secondary functions defined
below are given with explanation and examples in the
index file, so their definitions are simply
listed in the following.
spf =: +/@q: NB. sum of prime factors
snpf =: +/@~.@q: NB. sum of nub of prime factors
sopf =: +/@(1&,)@q: NB. sum of one and prime factors
sonpf =: +/@(1&,)@~.@q: NB. sum of one and nub of prime factors
pnpf =: */@~.@q: NB. product of nub of prime factors
This was not in the Encyclopedia, and has been accepted as
A074373.
It is A0014142
This was not in the Encyclopedia, and has been accepted as
A074374.
This was not in the Encyclopedia, and has been accepted as
A074375.
This is now
A074376.
sq =: *: NB. squares
tr =: -:@* >: NB. n(n+1)/2
ts =: -:@* 3&+ NB. n(n+3)/2
tt =: <:@-:@* 3&+ NB. n(n+3)/2 - 1
pt =: -:@* <:@*&3 NB. n(3n-1)/2
Geometric Sums of Prime Factors
sq spf 1+i.20 NB. square spf
0 4 9 16 25 25 49 36 36 49 121 49 169 81 64 64 289 64 361 81
tr spf 1+i.20 NB. triangular spf
0 3 6 10 15 15 28 21 21 28 66 28 91 45 36 36 153 36 190 45
ts spf 1+i.20 NB. triangular spf
0 5 9 14 20 20 35 27 27 35 77 35 104 54 44 44 170 44 209 54
pt spf 1+i.20 NB. pentagonal spf
0 5 12 22 35 35 70 51 51 70 176 70 247 117 92 92 425 92 532 117