cp's OEIS Frontend

A355529 Numbers of which it is not possible to choose a different prime factor of each prime index (with multiplicity).

%I A355529 #8 Jul 24 2022 14:13:39
%S A355529 2,4,6,8,9,10,12,14,16,18,20,21,22,24,25,26,27,28,30,32,34,36,38,40,
%T A355529 42,44,45,46,48,49,50,52,54,56,57,58,60,62,63,64,66,68,70,72,74,75,76,
%U A355529 78,80,81,82,84,86,88,90,92,94,96,98,99,100,102,104,105,106
%N A355529 Numbers of which it is not possible to choose a different prime factor of each prime index (with multiplicity).
%C A355529 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.
%C A355529 Includes all even numbers.
%e A355529 The terms together with their prime indices begin:
%e A355529     2: {1}
%e A355529     4: {1,1}
%e A355529     6: {1,2}
%e A355529     8: {1,1,1}
%e A355529     9: {2,2}
%e A355529    10: {1,3}
%e A355529    12: {1,1,2}
%e A355529    14: {1,4}
%e A355529    16: {1,1,1,1}
%e A355529    18: {1,2,2}
%e A355529    20: {1,1,3}
%e A355529    21: {2,4}
%e A355529    22: {1,5}
%e A355529    24: {1,1,1,2}
%t A355529 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A355529 Select[Range[100],Select[Tuples[primeMS/@primeMS[#]],UnsameQ@@#&]=={}&]
%Y A355529 The odd case is A355535.
%Y A355529 The case of all divisors (not just primes) is A355740, zeros of A355739.
%Y A355529 These choices are variously counted by A355741, A355744, A355745.
%Y A355529 A001414 adds up distinct prime divisors, counted by A001221.
%Y A355529 A003963 multiplies together the prime indices of n.
%Y A355529 A056239 adds up prime indices, row sums of A112798, counted by A001222.
%Y A355529 A120383 lists numbers divisible by all of their prime indices.
%Y A355529 A324850 lists numbers divisible by the product of their prime indices.
%Y A355529 A355731 counts choices of a divisor of each prime index, firsts A355732.
%Y A355529 Cf. A000720, A076610, A318979, A335433, A335448, A355733.
%K A355529 nonn
%O A355529 1,1
%A A355529 _Gus Wiseman_, Jul 24 2022