cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A117349 Near-multiperfects with primes, powers of 2 and 6 * prime excluded, abs(sigma(n) mod n) <= log(n).

Original entry on oeis.org

6, 10, 20, 28, 70, 88, 104, 110, 120, 136, 152, 464, 496, 592, 650, 672, 884, 1155, 1888, 1952, 2144, 4030, 5830, 8128, 8384, 8925, 11096, 17816, 18632, 18904, 30240, 32128, 32445, 32760, 32896, 33664, 45356, 70564, 77744, 85936, 91388, 100804, 116624
Offset: 1

Views

Author

Walter Nissen, Mar 09 2006

Keywords

Comments

Sequences A117346 through A117350 are an attempt to improve on sequences A045768 through A045770, A077374, A087167, A087485 and A088007 through A088012 and related sequences (but not to replace them) by using a more significant definition of "near." E.g., is sigma(n) really "near" a multiple of n, for n=9? Or n=18? Log is the natural logarithm. Sigma is the sum_of_divisors function.

Examples

			70 is a term because sigma(70) = 144 = 2*70 + 4, while 4 < log(70) ~= 4.248.

References

  • R. K. Guy, Unsolved Problems in Number Theory, B2.

Links

Crossrefs

Cf. A045768, A045769, A045770, A077374, A087167, A087485.
Cf. A088007, A088008, A088009, A088010, A088011, A088012.
Cf. A117346, A117347, A117348, A117350.

Formula

sigma(n) = k*n + r, abs(r) <= log(n).

Extensions

Offset corrected by Donovan Johnson, Oct 01 2012

A117350 Near-multiperfects with primes, powers of 2, 6 * prime and 2^n * prime excluded, abs(sigma(n) mod n) <= log(n).

Original entry on oeis.org

70, 110, 120, 650, 672, 884, 1155, 4030, 5830, 8925, 11096, 17816, 18632, 18904, 30240, 32445, 32760, 45356, 70564, 77744, 85936, 91388, 100804, 116624, 244036, 254012, 388076, 391612, 430272, 442365, 523776, 1090912, 1848964, 2178540
Offset: 1

Views

Author

Walter Nissen, Mar 09 2006

Keywords

Comments

Sequences A117346 through A117350 are an attempt to improve on sequences A045768 through A045770, A077374, A087167, A087485 and A088007 through A088012 and related sequences (but not to replace them) by using a more significant definition of "near." E.g., is sigma (n) really "near" a multiple of n, for n=9? Or n=18? Sigma is the sum_of_divisors function.

Examples

			70 is in the sequence because sigma(70) = 144 = 2*70 + 4, while 4 < log(70) ~= 4.248.
The 2-perfect numbers are excluded because they are 2^n * prime.

References

  • R. K. Guy, Unsolved Problems in Number Theory, B2.

Links

Crossrefs

Cf. A045768 through A045770, A077374, A087167, A087485, A088007 through A088012, A117346 through A117349.

Extensions

Offset corrected by Donovan Johnson, Oct 01 2012

A117347 Near-multiperfects with primes excluded, abs(sigma(m) mod m) <= log(m).

Original entry on oeis.org

4, 6, 8, 10, 16, 20, 28, 32, 64, 70, 88, 104, 110, 120, 128, 136, 152, 256, 464, 496, 512, 592, 650, 672, 884, 1024, 1155, 1888, 1952, 2048, 2144, 4030, 4096, 5830, 8128, 8192, 8384, 8925, 11096, 16384, 17816, 18632, 18904, 30240, 32128, 32445, 32760, 32768
Offset: 1

Views

Author

Walter Nissen, Mar 09 2006

Keywords

Comments

Sequences A117346 through A117350 are an attempt to improve on sequences A045768 through A045770, A077374, A087167, A087485 and A088007 through A088012 and related sequences (but not to replace them) by using a more significant definition of "near". E.g., is sigma(n) (where sigma is the sum-of-divisors function) really "near" a multiple of n, for n = 9? Or n = 18?

Examples

			70 is a term because sigma(70) = 144 = 2 * 70 + 4, while 4 < log(70) ~= 4.248.

References

  • R. K. Guy, Unsolved Problems in Number Theory, B2.

Links

Crossrefs

Cf. A045768, A045769, A045770, A077374, A087167, A087485.
Cf. A088007, A088008, A088009, A088010, A088011, A088012.
Cf. A117346, A117348, A117349, A117350.

Formula

sigma(m) = k * m + r, abs(r) <= log(m).

Extensions

Offset corrected by Amiram Eldar, Mar 05 2020

A117348 Near-multiperfects with primes and powers of 2 excluded, abs(sigma(m) mod m) <= log(m).

Original entry on oeis.org

6, 10, 20, 28, 70, 88, 104, 110, 120, 136, 152, 464, 496, 592, 650, 672, 884, 1155, 1888, 1952, 2144, 4030, 5830, 8128, 8384, 8925, 11096, 17816, 18632, 18904, 30240, 32128, 32445, 32760, 32896, 33664, 45356, 70564, 77744, 85936, 91388, 100804, 116624
Offset: 1

Views

Author

Walter Nissen, Mar 09 2006

Keywords

Comments

Sequences A117346 through A117350 are an attempt to improve on sequences A045768 through A045770, A077374, A087167, A087485 and A088007 through A088012 and related sequences (but not to replace them) by using a more significant definition of "near". E.g., is sigma(n) really "near" a multiple of n, for n = 9? Or n = 18? Sigma is the sum_of_divisors function.

Examples

			70 is a term because sigma(70) = 144 = 2 * 70 + 4, while 4 < log (70) ~= 4.248.

References

  • R. K. Guy, Unsolved Problems in Number Theory, B2.

Links

Crossrefs

Cf. A045768, A045769, A045770, A077374, A087167, A087485.
Cf. A088007, A088008, A088010, A088011, A088012.
Cf. A117346, A117347, A117349, A117350.

Formula

sigma(n) = k * n + r, abs(r) <= log(n).

Extensions

Offset corrected by Amiram Eldar, Mar 05 2020
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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