A097015 -id:A097015 - cp's OEIS frontend

A097011 Remainder of sigma(n) modulo 30.

1, 3, 4, 7, 6, 12, 8, 15, 13, 18, 12, 28, 14, 24, 24, 1, 18, 9, 20, 12, 2, 6, 24, 0, 1, 12, 10, 26, 0, 12, 2, 3, 18, 24, 18, 1, 8, 0, 26, 0, 12, 6, 14, 24, 18, 12, 18, 4, 27, 3, 12, 8, 24, 0, 12, 0, 20, 0, 0, 18, 2, 6, 14, 7, 24, 24, 8, 6, 6, 24, 12, 15, 14, 24, 4, 20, 6, 18, 20, 6, 1, 6

Offset: 1

Labos Elemer, Aug 19 2004

nonn

Indranil Ghosh, Table of n, a(n) for n = 1..10000

Cf. A084301, A084303, A000203, A097012, A097013, A097014, A097015.

Table[Mod[DivisorSigma[1, n], 30], {n, 120}] (* Michael De Vlieger, Jan 10 2017 *)

a(n) = sigma(n) % 30; \\ Michel Marcus, Dec 19 2013

a(n) = mod(A000203(n), 30).

A097012 a(n) = sigma(n) mod 210.

Original entry on oeis.org

1, 3, 4, 7, 6, 12, 8, 15, 13, 18, 12, 28, 14, 24, 24, 31, 18, 39, 20, 42, 32, 36, 24, 60, 31, 42, 40, 56, 30, 72, 32, 63, 48, 54, 48, 91, 38, 60, 56, 90, 42, 96, 44, 84, 78, 72, 48, 124, 57, 93, 72, 98, 54, 120, 72, 120, 80, 90, 60, 168, 62, 96, 104, 127, 84, 144, 68, 126, 96

Offset: 1

Labos Elemer, Aug 19 2004

nonn

Agrees with A000203(n) for n <= 89; sigma(90) = 234. - Omar E. Pol, Feb 02 2013

This sequence is not multiplicative. For example, at a(84) = 14 which is not a(3)*a(4)*a(7) = 224. - Andrew Howroyd, Aug 23 2018

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Cf. A000203, A084301, A084303, A097011, A097013, A097014, A097015.

[SumOfDivisors(n) mod 210: n in [1..70]]; // Vincenzo Librandi, Jul 25 2017

Array[Mod[DivisorSigma[1, #], 210] &, 69] (* Michael De Vlieger, Jul 24 2017 *)

a(n) = sigma(n) % 210; \\ Michel Marcus, Dec 19 2013

a(n) = A000203(n) mod 210.

A097014 Smallest x such that sigma(x) mod 210 = n.

Original entry on oeis.org

104, 1, 211, 2, 3, 8311689, 5, 4, 7, 3698, 399, 130321, 6, 9, 13, 8, 1477, 2458624, 10, 725904, 19, 676, 6751, 18766224, 14, 52707600, 489, 24649, 12, 220433409, 29, 16, 21, 1250, 2779, 3694084, 22, 5184, 37, 18, 27, 1382976, 20, 729, 43, 128, 217

Offset: 0

Labos Elemer, Aug 19 2004

Compare with A084303 and A097013.

Row 210 of A074625 (apart from different ordering). - Michel Marcus, Dec 19 2013

			Several numbers belonging to odd residues are either large squares or twice-squares.
E.g.: r = n = 209: a(209) = 36324729 = 6027^2, sigma(6027^2) = 210*172974 + 209.
Full set is easily available running through squares or twice squares.

Michel Marcus, Table of n, a(n) for n = 0..209

Cf. A000203, A084301, A084303, A097011, A097012, A097013, A097015.

A097013 Smallest x such that sigma(x) mod 30 = n.

Original entry on oeis.org

24, 1, 21, 2, 3, 923521, 5, 4, 7, 18, 27, 2401, 6, 9, 13, 8, 217, 9604, 10, 1089, 19, 98, 91, 21609, 14, 14641, 28, 49, 12, 2614689

Offset: 0

Labos Elemer, Aug 19 2004

Compare with A084303.

Row 30 of A074625 (apart from different ordering). - Michel Marcus, Dec 19 2013

Cf. A000203, A084301, A084303, A097011, A097012, A097014, A097015.

t=Table[Mod[DivisorSigma[1, w], 30], {w, 1, 2700000}]; Table[Min[Flatten[Position[t, j]]], {j, 0, 29}]

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A097011 Remainder of sigma(n) modulo 30.

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A097012 a(n) = sigma(n) mod 210.

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A097014 Smallest x such that sigma(x) mod 210 = n.

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A097013 Smallest x such that sigma(x) mod 30 = n.

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Mathematica