A097014 -id:A097014 - 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.

A097015 Smallest k such that sigma(k) + 1 is divisible by primorial(n).

Original entry on oeis.org

1, 1, 2401, 2614689, 36324729, 36324729, 2411675443849, 2411675443849, 12361036649679601

Offset: 0

Labos Elemer, Aug 19 2004

nonn

10^19 < a(9) <= 725298909352131113041. Terms a(3) through a(8) all have the prime signature p^4*q^2*r^2. Any x such that sigma(x) = -1 (mod 30) must have at least eight prime factors. However, for all n, there are solutions with fewer than three distinct prime factors. More generally, for any k > 1, let p be a prime of the form mk+1; then sigma(p^(k-2)) = -1 (mod k). For a(9), 725298909352131113041 is the least solution with eight prime factors. I have not been able to rule out a smaller solution with more prime factors. - David Wasserman, Dec 14 2007

Cf. A002110 (primorial), A084301, A084303, A000203, A097011, A097012, A097014, A233929.

a(n) = A233929(A002110(n)). - Andrew Howroyd, Dec 12 2024

More terms from David Wasserman, Dec 14 2007

a(0)=1 prepended by Andrew Howroyd, Dec 12 2024

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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A097015 Smallest k such that sigma(k) + 1 is divisible by primorial(n).

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

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