OFFSET
1,2
COMMENTS
The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
The augmented differences aug(y) of an integer partition y of length k are given by aug(y)_i = y_i - y_{i + 1} + 1 if i < k and aug(y)_k = y_k. For example, aug(6,5,5,3,3,3) = (2,1,3,1,1,3). Note that aug preserves length so this sequence preserves omega (number of prime factors counted with multiplicity).
LINKS
EXAMPLE
The partition (3,2,2,1) with Heinz number 90 has augmented differences (2,1,2,1) with Heinz number 36, so a(90) = 36.
MATHEMATICA
primeptn[n_]:=If[n==1, {}, Reverse[Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]];
aug[y_]:=Table[If[i<Length[y], y[[i]]-y[[i+1]]+1, y[[i]]], {i, Length[y]}];
Table[Times@@Prime/@aug[primeptn[n]], {n, 100}]
PROG
(PARI)
augdiffs(n) = { my(diffs=List([]), f=factor(n), prevpi, pi=0, i=#f~); while(i, prevpi=pi; pi = primepi(f[i, 1]); if(prevpi, listput(diffs, 1+(prevpi-pi))); if(f[i, 2]>1, f[i, 2]--, i--)); if(pi, listput(diffs, pi)); Vec(diffs); };
A325351(n) = factorback(apply(prime, augdiffs(n))); \\ Antti Karttunen, Nov 16 2019
CROSSREFS
KEYWORD
nonn,look
AUTHOR
Gus Wiseman, Apr 23 2019
EXTENSIONS
More terms from Antti Karttunen, Nov 16 2019
STATUS
approved