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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
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
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
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.)