OFFSET
1,2
COMMENTS
A binary carry of two positive integers is an overlap of the positions of 1's in their reversed binary expansion.
The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1) * ... * prime(y_k), so these are squarefree numbers whose prime indices have no carries. A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
EXAMPLE
The sequence of terms together with their prime indices begins:
1: {}
2: {1}
3: {2}
5: {3}
6: {1,2}
7: {4}
11: {5}
13: {6}
14: {1,4}
17: {7}
19: {8}
21: {2,4}
23: {9}
26: {1,6}
29: {10}
31: {11}
33: {2,5}
35: {3,4}
37: {12}
38: {1,8}
41: {13}
42: {1,2,4}
MATHEMATICA
binpos[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
stableQ[u_, Q_]:=!Apply[Or, Outer[#1=!=#2&&Q[#1, #2]&, u, u, 1], {0, 1}];
Select[Range[100], SquareFreeQ[#]&&stableQ[PrimePi/@First/@FactorInteger[#], Intersection[binpos[#1], binpos[#2]]!={}&]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 28 2019
STATUS
approved