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A325352
Heinz number of the differences plus one of the integer partition with Heinz number n.
31
1, 1, 1, 2, 1, 3, 1, 4, 2, 5, 1, 6, 1, 7, 3, 8, 1, 6, 1, 10, 5, 11, 1, 12, 2, 13, 4, 14, 1, 9, 1, 16, 7, 17, 3, 12, 1, 19, 11, 20, 1, 15, 1, 22, 6, 23, 1, 24, 2, 10, 13, 26, 1, 12, 5, 28, 17, 29, 1, 18, 1, 31, 10, 32, 7, 21, 1, 34, 19, 15, 1, 24, 1, 37, 6, 38
OFFSET
1,4
COMMENTS
The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
The only fixed point is 1 because otherwise the sequence decreases omega (A001222) by one.
EXAMPLE
The partition (3,2,2,1) with Heinz number 90 has differences plus one (2,1,2) with Heinz number 18, so a(90) = 18.
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
db[n_]:=Times@@Prime/@(1+Differences[primeMS[n]]);
Table[db[n], {n, 100}]
CROSSREFS
Positions of m's are A008578 (m = 1), A001248 (m = 2), A006094 (m = 3), A030078 (m = 4), A090076 (m = 5).
Sequence in context: A277895 A328772 A300726 * A305438 A078898 A246277
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 23 2019
STATUS
approved