A305055 Numbers n such that the z-density of the integer partition with Heinz number n is 0.

1, 169, 481, 507, 793, 841, 845, 1157, 1183, 1369, 1443, 1469, 1521, 1849, 1963, 2059, 2209, 2257, 2353, 2379, 2405, 2523, 2535, 2899, 3211, 3263, 3277, 3293, 3367, 3471, 3549, 3653, 3721, 3887, 3965, 4107, 4121, 4181, 4225, 4329, 4394, 4407, 4563, 4601, 4667

Offset

1,2

Comments

The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

The z-density of a multiset S of positive integers is Sum_{s in S} (omega(s) - 1) - omega(lcm(S)) where omega = A001221 is number of distinct prime factors.

Links

Table of n, a(n) for n=1..45.

Mathematica

zens[n_]:=If[n==1, 0, Total@Cases[FactorInteger[n], {p_, k_}:>k*(PrimeNu[PrimePi[p]]-1)]-PrimeNu[LCM@@Cases[FactorInteger[n], {p_, k_}:>PrimePi[p]]]];
Select[Range[1000], zens[#]==0&]

Crossrefs

Cf. A001221, A030019, A048143, A056239, A112798, A290103, A302242, A303837, A304118, A304714, A304716, A305001, A305052, A305053, A305054.

Sequence in context: A351337 A327652 A112076 * A069645 A294307 A017534

Adjacent sequences: A305052 A305053 A305054 * A305056 A305057 A305058

Keyword

nonn

Author

Gus Wiseman, May 24 2018

Status

approved