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A355749
Number of ways to choose a weakly decreasing sequence of divisors, one of each prime index of n (with multiplicity, taken in weakly increasing order).
7
1, 1, 2, 1, 2, 1, 3, 1, 3, 1, 2, 1, 4, 1, 2, 1, 2, 1, 4, 1, 3, 1, 3, 1, 3, 1, 4, 1, 4, 1, 2, 1, 2, 1, 3, 1, 6, 1, 3, 1, 2, 1, 4, 1, 3, 1, 4, 1, 6, 1, 2, 1, 5, 1, 2, 1, 3, 1, 2, 1, 6, 1, 4, 1, 4, 1, 2, 1, 2, 1, 6, 1, 4, 1, 2, 1, 3, 1, 4, 1, 5, 1, 2, 1, 2, 1, 3
OFFSET
1,3
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.
EXAMPLE
The a(2) = 1 through a(19) = 4 choices:
1 1 11 1 11 1 111 11 11 1 111 1 11 11 1111 1 111 1
2 3 2 21 5 2 21 7 2
4 22 3 4
6 8
MATHEMATICA
Table[Length[Select[Tuples[Divisors/@primeMS[n]], GreaterEqual@@#&]], {n, 100}]
CROSSREFS
Allowing any choice of divisors gives A355731, firsts A355732.
Choosing a multiset instead of sequence gives A355733, firsts A355734.
The reverse version is A355735, firsts A355736, only primes A355745.
A000005 counts divisors.
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.
A061395 selects the maximum prime index.
Sequence in context: A072625 A268187 A232440 * A278538 A282903 A332677
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 18 2022
STATUS
approved