The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A184395 a(n) = number of distinct values obtained when sigma is applied to the divisors of n. 5
 1, 2, 2, 3, 2, 4, 2, 4, 3, 4, 2, 6, 2, 4, 4, 5, 2, 6, 2, 6, 4, 4, 2, 8, 3, 4, 4, 6, 2, 8, 2, 6, 4, 4, 4, 9, 2, 4, 4, 8, 2, 8, 2, 6, 6, 4, 2, 10, 3, 6, 4, 6, 2, 8, 4, 8, 4, 4, 2, 12, 2, 4, 6, 7, 4, 7, 2, 6, 4, 8, 2, 12, 2, 4, 6, 6, 4, 8, 2, 10, 5, 4, 2, 12, 4, 4, 4, 8, 2, 12, 4, 6, 4, 4, 4, 12, 2, 6, 6, 9, 2, 8, 2, 8, 8, 4, 2, 12, 2, 8, 4, 10, 2, 8, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Sequence is not the same as A000005(n): a(66) = 7, A000005(66) = 8. a(n) = number of numbers k <= sigma(n) such that k = sigma(d) for some divisor d of n, where sigma = A000203. - This is the original name of the sequence, except that I substituted "some divisor" for "any divisor". - Antti Karttunen, Aug 24 2017 LINKS Antti Karttunen, Table of n, a(n) for n = 1..10000 FORMULA a(n) = A000203(n) - A184396(n). EXAMPLE For n = 4, sigma(4) = 7, from numbers 1 - 7 there are three numbers k such that k = sigma(d) for any divisor d of n: 1 = sigma(1), 3 = sigma(2), 7 = sigma(4); a(4) = 3. From Antti Karttunen, Aug 24 2017: (Start) For n = 66, its 8 divisors are [1, 2, 3, 6, 11, 22, 33, 66]. When applying sigma to these, we obtain [1, 3, 4, 12, 12, 36, 48, 144], with one duplicate present, thus there are only 8-1 = 7 distinct values and a(66) = 7. For n = 70, its 8 divisors are [1, 2, 5, 7, 10, 14, 35, 70]. When applying sigma to these, we obtain [1, 3, 6, 8, 18, 24, 48, 144], which are all unique values, thus a(70) = 8. (End) PROG (PARI) A184395(n) = length(vecsort(apply(d->sigma(d), divisors(n)), , 8)); \\ Antti Karttunen, Aug 24 2017 CROSSREFS Cf. A000005, A000203, A184396. Sequence in context: A335519 A167447 A134687 * A329484 A179941 A179942 Adjacent sequences:  A184392 A184393 A184394 * A184396 A184397 A184398 KEYWORD nonn AUTHOR Jaroslav Krizek, Jan 12 2011 EXTENSIONS Name changed, a(66) and a(70) corrected and more terms added by Antti Karttunen, Aug 24 2017 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 2 21:30 EDT 2021. Contains 346429 sequences. (Running on oeis4.)