A385402 -id:A385402 - cp's OEIS frontend

A385858 Numbers m in A385402 which are not prime.

1, 35, 77, 95, 119, 125, 143, 187, 209, 221, 247, 259, 299, 319, 323, 377, 391, 403, 427, 437, 473, 493, 527, 551, 589, 629, 667, 697, 713, 731, 779, 799, 817, 851, 893, 899, 943, 989, 1007, 1073, 1139, 1147, 1189, 1199, 1219, 1247, 1271, 1313, 1333, 1343, 1357, 1363, 1387, 1397

Offset: 1

Robert G. Wilson v, Jul 10 2025

nonn

Since all the primes are in A385402, this sequence is more concise.

Cf. A018804, A384628, A385398.

Proper subset of A385402.

fQ[m_] := Sum[ GCD[m, Floor[m/k]], {k, m}] == Sum[ GCD[m, Ceiling[m/k]], {k, m}]; j = 1; lst = {}; While[j < 1400, If[ !PrimeQ@ j && fQ@ j, AppendTo[lst, j]]; j++]; lst

isok(m) = if (!isprime(m), sum(k=1, m, gcd(m, floor(m/k))) == sum(k=1, m, gcd(m, ceil(m/k)))); \\ Michel Marcus, Jul 10 2025

A385398 Numbers m >= 1 such that Sum_{k = 1..m} gcd(m, floor(m / k)) > Sum_{k = 1..m} gcd(m, ceiling(m / k)).

Original entry on oeis.org

407, 539, 559, 637, 671, 793, 803, 949, 1037, 1067, 1159, 1241, 1273, 1331, 1469, 1649, 1679, 1727, 1817, 1843, 1853, 1919, 2057, 2159, 2197, 2231, 2299, 2321, 2507, 2651, 2669, 2743, 2783, 2813, 2873, 2983, 2987, 3007, 3077, 3133, 3161, 3179, 3193, 3211, 3379

Offset: 1

Ctibor O. Zizka, Jun 27 2025

nonn

			m = 407: Sum_{k = 1..407} gcd(407, floor(407 / k)) = 909, Sum_{k = 1..407} gcd(407, ceiling(407 / k)) = 899, 909 > 899, thus m = 407 is a term.

Cf. A018804, A384628, A385402.

isok(m) = sum(k=1, m, gcd(m, floor(m/k))) > sum(k=1, m, gcd(m, ceil(m/k))); \\ Michel Marcus, Jun 28 2025

cp's OEIS Frontend

A385858 Numbers m in A385402 which are not prime.

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