A055009 -id:A055009 - cp's OEIS frontend

A084293 a(n) = 2n + A054905(n).

436, 305635361, 110, 35, 195566, 77, 26, 55, 38, 76, 938, 104, 212308, 85, 74, 106677, 86, 161

Offset: 1

Labos Elemer, May 26 2003

The sequence begins 436, 305635361, 110, 35, 195566, 77, 26, 55, 38, 76, 938, 104, 212308, 85, 74, 106677, 86, 161, ?, 91, 87, 92, 122, 111, 1585396, 145, 94, 76627, 10283, 159, 772, 133, 122, 412, 194, 142, 964, 205, 374, 925, 6725, 209, ?, 1015, 178, ?, ?, 206, 146, ?, ..., where the other missing terms (designated by "?") are unknown, if they exist (see also A206768).

			To terms of A054905, where sigma(x+2n)=sigma(x)+2n replacing x+2n=y,x=y-2n, we get sigma(y)-2n=sigma(y-2n);
For several analogous sequences, the corresponding "mirror-solutions" can be easily constructed. See: e.g. A015913-A015918; A050507, A054799, A054903-A054906; A054982-A054987; A059118; A055009, A055458, A063500, etc.

Cf. A054905.

Composite x satisfying sigma(x-2n) = sigma(x) - 2n.

A084292 a(n) = 6n + A054904(n).

Original entry on oeis.org

110, 77, 38, 104, 74, 161, 87, 111, 94, 159, 122, 142, 374, 209, 178, 206, 206, 253, 326, 302, 206, 302, 471, 249, 519, 341, 346, 303, 354, 481, 542, 377, 2057, 533, 386, 411, 5138, 662, 846, 527, 386, 437, 1034, 519, 794, 689, 626, 493, 566, 629, 873, 527, 638

Offset: 1

Labos Elemer, May 26 2003

nonn

Composite solutions y to sigma(y-6n) = sigma(y) - 6n. For terms x of A054904, where sigma(x+6n) = sigma(x) + 6n, replacing x+6n = y, x = y-6n, we get sigma(y) - 6n = sigma(y-6n).

Amiram Eldar, Table of n, a(n) for n = 1..724

Cf. A000203 (sigma), A054904, A084293.

For several analogous sequences such corresponding "mirror-solutions" can be easily constructed. See, e.g., A015913-A015918, A050507, A054799, A054903-A054906, A054982-A054987, A059118, A055009, A055458, A063500, etc.

A055036 Min[x] composite zero site for sigma(x+6^n) - sigma(x) - 6^n.

Original entry on oeis.org

104, 125, 195, 415, 2743, 2935, 3535, 19735, 22645, 108703, 977353, 1921033, 2523433, 2425175, 4227575, 85969345, 32606935, 224917033, 1362833713, 716210677, 1557843865, 6226853857, 20369543065

Offset: 1

Labos Elemer, Jun 01 2000

			n = 6: d = 6^6 = 46656, a(n) = a(6) = 2935 because sigma(2935) + 46656 = 1 + 5 + 587 + 2935 + 46656 = sigma(2935 + 46656) = sigma(49591) = 1 + 101 + 491 + 49591 = 50184.

Subsequence of A054904.

Cf. A054902-A054905, A054799, A054982-A054985, A054987, A055009, A015913-A015518.

L = {}; Do[i = 1; While[ ! ((Plus @@ Divisors[i + 6^j] == 6^j + Plus @@ Divisors[i]) && ! PrimeQ[i]), i++ ]; L = Append[L, i], {j, 1, 11}]; L (from Vit Planocka)

a(n) = Min(x) solution for A000203(x+A000400(n)) = A000203(x) + A000400(n) Diophantine equation.

One more term from Vit Planocka (planocka(AT)mistral.cz), Sep 23 2003

a(12)-a(23) from Donovan Johnson, Nov 30 2008

cp's OEIS Frontend

A084293 a(n) = 2n + A054905(n).

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A084292 a(n) = 6n + A054904(n).

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A055036 Min[x] composite zero site for sigma(x+6^n) - sigma(x) - 6^n.

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