OFFSET
1,6
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 partition (3,2,2,1) has Heinz number 90, so a(90) = 3. The partition (3,3,1,1) has Heinz number 100, so a(100) = 4.
MATHEMATICA
pnq[y_]:=Length[Select[Range[Length[y]], #!=y[[#]]&]];
Table[pnq[Reverse[If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]]], {n, 100}]
PROG
(PARI) A352825(n) = { my(f=factor(n), i=bigomega(n), c=0); for(k=1, #f~, while(f[k, 2], f[k, 2]--; c += (i!=primepi(f[k, 1])); i--)); (c); }; \\ Antti Karttunen, Apr 14 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 05 2022
EXTENSIONS
Data section extended up to 105 terms by Antti Karttunen, Apr 14 2022
STATUS
approved