OFFSET
1,2
COMMENTS
The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
The enumeration of these partitions by sum is given by A018818.
LINKS
R. J. Mathar, Table of n, a(n) for n = 1..543
EXAMPLE
The sequence of terms together with their prime indices begins:
1: {}
2: {1}
3: {2}
4: {1,1}
5: {3}
7: {4}
8: {1,1,1}
9: {2,2}
11: {5}
12: {1,1,2}
13: {6}
16: {1,1,1,1}
17: {7}
19: {8}
23: {9}
25: {3,3}
27: {2,2,2}
29: {10}
30: {1,2,3}
31: {11}
MAPLE
isA326841 := proc(n)
local ifs, psigsu, p, psig ;
psigsu := A056239(n) ;
for ifs in ifactors(n)[2] do
p := op(1, ifs) ;
psig := numtheory[pi](p) ;
if modp(psigsu, psig) <> 0 then
return false;
end if;
end do:
true;
end proc:
for i from 1 to 3000 do
if isA326841(i) then
printf("%d %d\n", n, i);
n := n+1 ;
end if;
end do: # R. J. Mathar, Aug 09 2019
MATHEMATICA
Select[Range[100], With[{y=If[#==1, {}, Flatten[Cases[FactorInteger[#], {p_, k_}:>Table[PrimePi[p], {k}]]]]}, And@@IntegerQ/@(Total[y]/y)]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 26 2019
STATUS
approved