A202275 -id:A202275 - cp's OEIS frontend

A202276 Number of integers k <= n such that sigma(x) = k has no solution, sigma = A000203.

0, 1, 1, 1, 2, 2, 2, 2, 3, 4, 5, 5, 5, 5, 5, 6, 7, 7, 8, 8, 9, 10, 11, 11, 12, 13, 14, 14, 15, 15, 15, 15, 16, 17, 18, 18, 19, 19, 19, 19, 20, 20, 21, 21, 22, 23, 24, 24, 25, 26, 27, 28, 29, 29, 30, 30, 30, 31, 32, 32, 33, 33, 33, 34, 35, 36, 37, 37, 38, 39

Offset: 1

Jaroslav Krizek, Dec 25 2011

nonn

Partial sums of A175253.

			a(9) = 3 because sigma(x) = k has no solution for k = 2, 5 and 9.

Jaroslav Krizek, Table of n, a(n) for n = 1..10000

Cf. A074753, A202277, A202275, A175523, A007369, A007368, A007609.

seq[max_] := Module[{t = Table[0, {max}]}, t[[Complement[Range[max], Table[ DivisorSigma[1, n], {n, 1, max}]]]] = 1; Accumulate@ t]; seq[100] (* Amiram Eldar, Dec 20 2024 *)

A175253 a(n) = characteristic function of numbers k such that A000203(m) = k has no solution for any m, where A000203(m) = sum of divisors of m.

Original entry on oeis.org

0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1

Offset: 1

Jaroslav Krizek, Mar 14 2010

nonn

a(n) = characteristic function of numbers from A007369(n). a(n) = 1 if A000203(m) not equal to n for any m, else 0. a(n) = 1 for such n that A054973(n) = 0. a(n) = 0 for such n that A054973(n) >= 1. a(n) + A175192(n) = A000012(n).

Jaroslav Krizek, Table of n, a(n) for n = 1..10000

Cf. A074753, A202275, A202276, A175523, A007369, A007368, A007609.

seq[max_] := Module[{t = Table[0, {max}]}, t[[Complement[Range[max], Table[ DivisorSigma[1, n], {n, 1, max}]]]] = 1; t]; seq[100] (* Amiram Eldar, Mar 22 2024 *)

More terms from Jaroslav Krizek, Dec 25 2011.

A202277 Numbers m such that number of integers k such sigma(k) <= m (A074753) is equal to number of integers k <= m such that sigma(x) = k has no solution (A202276).

Original entry on oeis.org

2, 537, 639, 647, 653, 655, 657, 661, 663, 672, 674, 684, 686

Offset: 1

Jaroslav Krizek, Dec 25 2011

nonn

Numbers m such that A074753(m) - A202276(m) = 0.
Numbers m such that A202275(m) = 0 (see graph of A202275).
Conjecture: sequence is finite with 13 terms.

Cf. A074753, A202275, A202276, A175523, A007369, A007368, A007609.

cp's OEIS Frontend

A202276 Number of integers k <= n such that sigma(x) = k has no solution, sigma = A000203.

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A175253 a(n) = characteristic function of numbers k such that A000203(m) = k has no solution for any m, where A000203(m) = sum of divisors of m.

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A202277 Numbers m such that number of integers k such sigma(k) <= m (A074753) is equal to number of integers k <= m such that sigma(x) = k has no solution (A202276).

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