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 1-3 of 3 results.

A336296 The least prime p such that equation x = p*sopf(x) (where sopf(x) is the sum of distinct prime factors of x) has exactly n solutions in positive integers.

Original entry on oeis.org

2, 3, 7, 19, 71, 431, 1259, 4679, 9719, 23399, 7559, 42839, 134399, 181439, 477359, 241919, 262079, 453599
Offset: 1

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Author

Vladimir Letsko, Jul 16 2020

Keywords

Comments

It seems that a(n) is the least number for which equation x = p*sopf(x) has exactly n solutions in positive integers not only for prime numbers.

Examples

			a(3) = 7 because there are 3 solutions of the equation x = 7*sopf(x), which are {49, 84, 105}, and this is the smallest prime that gives 3 solutions.

Links

Crossrefs

Cf. A008472, A089352, A336098, A336099, A336297, A157190 (note overlap of values).

A336445 Integers m such that m/sopf(m) is a prime number where sopf(m) is A008472(m), the sum of the distinct primes dividing m.

Original entry on oeis.org

4, 9, 25, 30, 49, 70, 84, 105, 121, 169, 231, 234, 260, 286, 289, 361, 456, 529, 532, 627, 646, 805, 841, 897, 961, 1116, 1364, 1369, 1581, 1665, 1681, 1798, 1849, 1924, 2064, 2150, 2209, 2632, 2809, 2967, 3055, 3339, 3481, 3526, 3721, 4489, 4543, 4824, 5025, 5041
Offset: 1

Views

Author

Michel Marcus, Jul 22 2020

Keywords

Comments

All squares of primes (A001248) are terms.

Examples

			4 is a term since sopf(4)=2 and 4/2 = 2 is a prime.
30 is a term since sopf(30)=10 and 30/10 = 3 is a prime.

Links

Crossrefs

Cf. A008472 (sopf).
Subsequence of A071139.
A001248 is a subsequence.
Cf. A336296, A336297.

Programs

  • PARI
    sopf(n)=vecsum(factor(n)[, 1]); \\ A008472
isokp(k) = my(q=k/sopf(k)); (denominator(q)==1) && isprime(q);

A336493 a(n) is the largest integer x such that x/sopf(x) = prime(n) where sopf(x) is the sum of distinct prime factors of x and prime(n) is the n-th prime.

Original entry on oeis.org

4, 30, 70, 105, 286, 260, 646, 627, 897, 1798, 1581, 1924, 3526, 2967, 3055, 3339, 7198, 3721, 6164, 10366, 5840, 9717, 10707, 9256, 9409, 20806, 16377, 23326, 16132, 12769, 21844, 26331, 38086, 29607, 44998, 22801, 33284, 40587, 35905, 29929, 64798, 44164, 73726
Offset: 1

Views

Author

Michel Marcus, Jul 23 2020

Keywords

Comments

For the primes p=prime(m) that are in A336297, a(m) = prime(m)^2.

Examples

			For the 4th prime p=7, the 3 integers (49,84,105) satisfy x/sopf(x)=7, so a(4)=105.

Crossrefs

Cf. A008472.
Subsequence of A336445.
Cf. A336296, A336297.
Showing 1-3 of 3 results.

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

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