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

2, 4, 6, 8, 9, 10, 12, 14, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 34, 36, 38, 40, 42, 44, 45, 46, 48, 49, 50, 52, 54, 56, 57, 58, 60, 62, 63, 64, 66, 68, 70, 72, 74, 75, 76, 78, 80, 81, 82, 84, 86, 88, 90, 92, 94, 96, 98, 99, 100, 102, 104, 105, 106

Offset

1,1

Comments

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.

Includes all even numbers.

Links

Table of n, a(n) for n=1..65.

Example

The terms together with their prime indices begin:
    2: {1}
    4: {1,1}
    6: {1,2}
    8: {1,1,1}
    9: {2,2}
   10: {1,3}
   12: {1,1,2}
   14: {1,4}
   16: {1,1,1,1}
   18: {1,2,2}
   20: {1,1,3}
   21: {2,4}
   22: {1,5}
   24: {1,1,1,2}

Mathematica

primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], Select[Tuples[primeMS/@primeMS[#]], UnsameQ@@#&]=={}&]

Crossrefs

The odd case is A355535.

The case of all divisors (not just primes) is A355740, zeros of A355739.

These choices are variously counted by A355741, A355744, A355745.

A001414 adds up distinct prime divisors, counted by A001221.

A003963 multiplies together the prime indices of n.

A056239 adds up prime indices, row sums of A112798, counted by A001222.

A120383 lists numbers divisible by all of their prime indices.

A324850 lists numbers divisible by the product of their prime indices.

A355731 counts choices of a divisor of each prime index, firsts A355732.

Cf. A000720, A076610, A318979, A335433, A335448, A355733.

Sequence in context: A153184 A047412 A282760 * A355670 A336375 A353683

Adjacent sequences: A355526 A355527 A355528 * A355530 A355531 A355532

Keyword

nonn

Author

Gus Wiseman, Jul 24 2022

Status

approved