A358253 - OEIS

%I #20 Nov 06 2022 03:17:11

%S 1,8,32,128,288,864,1152,2592,4608,10368,20736,28800,41472,64800,

%T 115200,259200,518400,1036800,2073600,4147200,8294400,9331200,

%U 12700800,25401600,50803200,101606400,203212800,406425600,457228800,635040000,812851200,914457600,1270080000

%N Numbers with a record number of non-unitary square divisors.

%C Numbers m such that A056626(m) > A056626(k) for all k < m.

%C The corresponding record values are 0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 16, 20, 22, ... (see the link for more values).

%H Amiram Eldar, <a href="/A358253/b358253.txt">Table of n, a(n) for n = 1..283</a>

%H Amiram Eldar, <a href="/A358253/a358253_1.txt">Table of n, a(n), A056626(a(n)) for n = 1..283</a>

%t f1[p_, e_] := 1 + Floor[e/2]; f2[p_, e_] := 2^(1 - Mod[e, 2]); f[1] = 0; f[n_] := Times @@ f1 @@@ (fct = FactorInteger[n]) - Times @@ f2 @@@ fct; s = {}; fmax = -1; Do[If[(fn = f[n]) > fmax, fmax = fn; AppendTo[s, n]], {n, 1, 10^5}]; s

%o (PARI) s(n) = {my(f = factor(n)); prod(i = 1, #f~, 1 + floor(f[i,2]/2)) - 2^sum(i = 1, #f~, 1 - f[i,2]%2);}

%o lista(nmax) = {my(smax = -1, sn); for(n = 1, nmax, sn = s(n); if(sn > smax, smax = sn; print1(n, ", "))); }

%Y Cf. A056626, A358252.

%Y Subsequence of A025487.

%Y Similar sequences: A002182 (all divisors), A002110 (unitary), A037992 (infinitary), A046952 (square divisors), A053624 (odd divisors), A293185 (bi-unitary), A309141 (non-unitary), A318278 (exponential).

%K nonn

%O 1,2

%A _Amiram Eldar_, Nov 05 2022