A325352 Heinz number of the differences plus one of the integer partition with Heinz number n.

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.

Links

Table of n, a(n) for n=1..76.

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).

Cf. A007294, A049988, A056239, A093641, A112798, A240026, A320466, A325328, A325351, A325360, A325361, A325368, A325405.

Sequence in context: A277895 A328772 A300726 * A305438 A078898 A246277

Adjacent sequences: A325349 A325350 A325351 * A325353 A325354 A325355

Keyword

nonn

Author

Gus Wiseman, Apr 23 2019

Status

approved