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. A subset-sum of an integer partition is any sum of a submultiset of it.
The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), so these are Heinz numbers of the partitions counted by A325835.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
The sequence of terms together with their prime indices begins:
12: {1,1,2}
30: {1,2,3}
40: {1,1,1,3}
63: {2,2,4}
70: {1,3,4}
112: {1,1,1,1,4}
154: {1,4,5}
165: {2,3,5}
198: {1,2,2,5}
220: {1,1,3,5}
273: {2,4,6}
286: {1,5,6}
325: {3,3,6}
351: {2,2,2,6}
352: {1,1,1,1,1,5}
364: {1,1,4,6}
442: {1,6,7}
525: {2,3,3,4}
550: {1,3,3,5}
561: {2,5,7}
MAPLE
filter:= proc(n) local F, t, S, i;
F:= map(t -> [numtheory:-pi(t[1]), t[2]], ifactors(n)[2]);
S:= {0}:
for t in F do
S:= map(s -> seq(s + i*t[1], i=0..t[2]), S);
od;
nops(S) = mul(t[2]+1, t=F)-1
end proc:
select(filter, [$1..2000]); # Robert Israel, Oct 30 2024
MATHEMATICA
Select[Range[100], DivisorSigma[0, #]==1+Length[Union[hwt/@Divisors[#]]]&]
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
Gus Wiseman, May 23 2019
STATUS
approved