A352797 - OEIS

%I #27 May 11 2022 10:29:36

%S 1,3,9,45,135,945,2835,14175,155925,467775,6081075

%N Let S(k) be the subsequence of multiples of k from k*positive integers where each element of S(k) sets a new record of divisors in that sequence. Then f(k) is the first element from S(k)/k that is not a power of 2. Sequence lists records for f(k).

%C Conjecture: Subsequence of A147516.

%e For k=1, the sequence of multiples of 1 that set records for numbers of divisors (divided by 1) starts 1,2,4,6. (A002182)

%e For k=3, the sequence starts 1,2,4,8,12. (A351623)

%e For k=9, the sequence starts 1,2,4,8,16,20.

%e For k=45, the sequence starts 1,2,4,8,16,24.

%o (PARI) isp2(n) = if (n<=2, return(1)); my(m); ispower(n,,&m) && (m==2);

%o f(n) = {my(m=1, nm, k=1, ok=0); until(ok, nm = numdiv(k*n); if (nm > m, m = nm; if (!isp2(k), ok = 1);); if (!ok, k++);); k;}

%o lista(nn) = {my(m=1, fm); for (n=1, nn, fm = f(n); if (fm > m, m = fm; print1(n, ", ");););} \\ _Michel Marcus_, May 05 2022

%Y Cf. A002182, A351623, A147516.

%K nonn,more

%O 1,2

%A _J. Lowell_, Apr 03 2022