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 A358253 Numbers with a record number of non-unitary square divisors. 3
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified May 22 02:24 EDT 2024. Contains 372741 sequences. (Running on oeis4.)