A327503 -id:A327503 - cp's OEIS frontend

A351948 Numbers k for which A327503(A046523(k)) differs from A327503(k).

125000, 941192, 8000000, 14172488, 16000000, 28344976, 38614472, 47832147, 60236288, 77228944, 120472576, 130323843, 193100552, 312500000, 376367048, 386201104, 625000000, 651714363, 752734096, 907039232, 1184287112, 1270238787, 1814078464, 1953125000, 2368574224, 2471326208, 3996969003

Offset: 1

Antti Karttunen, Apr 03 2022

nonn

Each term is a perfect power (in A001597).

Cf. A046523, A327503.

Subsequence of A001597.

A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
A327502(n) = if(n==1, 1, n/vecmax(select(x->((x>1) && !ispower(x)), divisors(n))));
A327503(n) = { my(u=A327502(n)); if(u==n, 0, 1+A327503(u)); };
isA351948(k) = if(!ispower(k),0,(A327503(A046523(k)) != A327503(k)));

A327500 Number of steps to reach a fixed point starting with n and repeatedly taking the quotient by the maximum divisor whose prime multiplicities are distinct (A327498, A327499).

Original entry on oeis.org

0, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 2, 2, 2, 2, 1, 2, 2, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 1, 2, 3, 1, 1, 2, 3, 1, 1, 1, 2, 1, 1, 2, 3, 1, 1, 1, 2, 1, 2, 2, 2, 2, 1, 1, 2, 2, 1, 2, 2, 2, 1, 1, 1, 1, 2, 1, 3, 1, 1, 3

Offset: 1

Gus Wiseman, Sep 16 2019

nonn

A number's prime multiplicities are also called its (unsorted) prime signature. Numbers whose prime multiplicities are distinct are A130091.

			We have 9282 -> 546 -> 42 -> 6 -> 2 -> 1, so a(9282) = 5.

Antti Karttunen, Table of n, a(n) for n = 1..65537
Gus Wiseman, Sequences counting and encoding certain classes of multisets

See link for additional cross-references.
Position of first appearance of n is A002110(n).
Cf. A000005, A056239, A098859, A112798, A124010, A130091, A255231, A327498, A327499, A351564.
Cf. also A327503.

Table[Length[FixedPointList[#/Max[Select[Divisors[#],UnsameQ@@Last/@FactorInteger[#]&]]&,n]]-2,{n,100}]

A351564(n) = issquarefree(factorback(apply(e->prime(e),(factor(n)[,2]))));
A327499(n) = fordiv(n,d,if(A351564(n/d), return(d)));
A327500(n) = { my(u=A327499(n)); if(u==n, 0, 1+A327500(u)); }; \\ Antti Karttunen, Apr 02 2022

Data section extended up to 105 terms by Antti Karttunen, Apr 02 2022

cp's OEIS Frontend

A351948 Numbers k for which A327503(A046523(k)) differs from A327503(k).

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A327500 Number of steps to reach a fixed point starting with n and repeatedly taking the quotient by the maximum divisor whose prime multiplicities are distinct (A327498, A327499).

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