A358253 Numbers with a record number of non-unitary square divisors.

1, 8, 32, 128, 288, 864, 1152, 2592, 4608, 10368, 20736, 28800, 41472, 64800, 115200, 259200, 518400, 1036800, 2073600, 4147200, 8294400, 9331200, 12700800, 25401600, 50803200, 101606400, 203212800, 406425600, 457228800, 635040000, 812851200, 914457600, 1270080000

Offset

1,2

Comments

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

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).

Links

Amiram Eldar, Table of n, a(n) for n = 1..283

Amiram Eldar, Table of n, a(n), A056626(a(n)) for n = 1..283

Mathematica

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

Prog

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

Crossrefs

Cf. A056626, A358252.

Subsequence of A025487.

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

Sequence in context: A183915 A357789 A363333 * A358252 A325839 A081654

Adjacent sequences: A358250 A358251 A358252 * A358254 A358255 A358256

Keyword

nonn

Author

Amiram Eldar, Nov 05 2022

Status

approved