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.

A126028 Perfect square roots: numbers n such that (sopfr(n)*d(n))^2 = sigma(n) where sopfr = sum of prime factors with multiplicity (A001414), d(n) = number of divisors of n, sigma(n) = sum of divisors of n.

Original entry on oeis.org

22446139, 26116291, 28097023, 30236557, 31090489, 31124341, 49941589, 61137673, 62224039, 66960589, 71334867, 71585139, 82266591, 83045869, 88658031, 92346023, 92837591, 105183961, 114762567, 123563821, 129616270, 130399138, 131494219, 134156197
Offset: 1

Views

Author

Fred Schneider, Dec 14 2006

Keywords

Examples

			n = 22446139 = 31*67*101*107. sopfr(n) = 31+67+101+107 = 306, d(n) = 2^4 = 16, sigma(n) = (31+1)*(67+1)*(101+1)*(107+1) = 23970816, (sopfr(n)*d(n))^2 = (306*16)^2 = 23970816 = sigma(n).

Links

Crossrefs

Subsequence of A006532. Cf. A126029, A008472, A000005, A000203, A001414, A226479, A226480.

Extensions

Clarified and extended by Charles R Greathouse IV, Oct 11 2009
Clarified by Donovan Johnson, Jun 09 2013

A226480 Squarefree numbers n such that (sopf(n)*d(n))^2 = sigma(n) where sopf(n) = sum of prime factors of n and d(n) = number of divisors of n.

Original entry on oeis.org

22446139, 26116291, 28097023, 30236557, 31090489, 31124341, 49941589, 61137673, 62224039, 66960589, 71334867, 71585139, 82266591, 83045869, 92346023, 92837591, 105183961, 114762567, 123563821, 130399138, 131494219, 134156197, 134867722, 135095767, 136026037
Offset: 1

Views

Author

Donovan Johnson, Jun 09 2013

Keywords

Comments

Suggested by N. J. A. Sloane.

Examples

			n = 22446139 = 31*67*101*107. sopf(n) = 31+67+101+107 = 306. d(n) = 16. (sopf(n)*d(n))^2 = (306*16)^2 = 23970816 = sigma(n).

Links

Crossrefs

Cf. A000005, A000203, A006532, A008472, A126028, A226479.

A126029 The smallest positive k such that ( sopfr(k)*tau(k) )^n = sigma(k) where sopfr is the sum of prime factors with multiplicity (A001414).

Original entry on oeis.org

35, 22446139, 4481106818619089
Offset: 1

Views

Author

Fred Schneider, Dec 14 2006

Keywords

Comments

35 is the only solution for n=1.
Incorrect, there are three solutions < 10^10 for n = 1: 35, 42 and 68. - Donovan Johnson, Jun 11 2013
a(3) = 14844221560107739 (conjectured) is most likely minimal but it hasn't been proved. No solutions have been found (minimal or otherwise) where the number was not squarefree.
a(3) <= 4481106818619089. - Donovan Johnson, Jun 10 2013

Examples

			22446139 factors as: 31*67*101*107=k, sopfr(k) = sum of prime factors of k = 31+67+101+107 = 306. tau(k) = num of divisors of k = 2^4 = 16. sigma(k) = sum of divisors of k = (31+1)*(67+1)*(101+1)*(107+1) = 23970816. (306*16)^2 = 23970816. As this k turns out to be minimal, a(2)=22446139.

Links

Crossrefs

Cf. A126028, A000005, A000203, A001414, A226479, A226480.

Formula

min {k : (A001414(k)*A000005(k))^n = A000203(k)}. - R. J. Mathar, Jun 04 2013

Extensions

New name from R. J. Mathar, Jun 04 2013
a(3) from Hiroaki Yamanouchi, Sep 26 2014
Showing 1-3 of 3 results.

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

Content is available under The OEIS End-User License Agreement.