login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A355571 Complement of A007956: numbers not of the form P(k)/k where P(n) is the product of the divisors of n. 0
4, 9, 12, 16, 18, 20, 24, 25, 28, 30, 32, 36, 40, 42, 44, 45, 48, 49, 50, 52, 54, 56, 60, 63, 66, 68, 70, 72, 75, 76, 78, 80, 81, 84, 88, 90, 92, 96, 98, 99, 100, 102, 104, 105, 108, 110, 112, 114, 116, 117, 120, 121, 124, 126, 128, 130, 132, 135, 136, 138, 140, 147, 148, 150, 152 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
There are no primes in the sequence, since A007956(p^2) = p for all primes p.
There are infinitely many terms, in fact p^2 is a term for all primes p.
If 8k+1 is not a perfect square, then p^k is a term for all primes p.
Depends only on the prime signature: n is in this sequence if and only if A046523(n) is in this sequence. - Charles R Greathouse IV, Jul 08 2022
Contains all the weak numbers (A052485) aside from the primes (A000040) and squarefree semiprimes (A006881). - Charles R Greathouse IV, Jul 08 2022
REFERENCES
Wacław Sierpiński, Elementary Theory of Numbers, Ex. 2 p. 174, Warsaw, 1964.
LINKS
FORMULA
a(n) = n + O(n log log n/log n). - Charles R Greathouse IV, Jul 08 2022
EXAMPLE
4 is a term of this sequence because there are no numbers k such that A007956(k) = 4.
2^10 is not a term of this sequence because A007956(32) = 1024 (Note that 8*10+1=81=9^2 is a perfect square).
p^4 belongs to this sequence for all primes p, in fact 8*4+1=33 is not a perfect square, so there are no numbers h such that A007956(h) = p^4.
MATHEMATICA
Complement[Complement[Table[n, {n, 2, 1000}], Select[NumericalSort[Table[Times @@ Most[Divisors[n]], {n, 1000000}]], # != 1 && # < 1000 &]], Select[Table[Prime[n], {n, 1, 1000}], # < 1000 &]]
CROSSREFS
Subsequences by prime signature: A001248 (p^2), A054753 (p^2*q), A030514 (p^4), A065036 (p^3*q), A007304 (p*q*r), A050997 (p^5), A085986 (p^2*q^2).
Sequence in context: A010386 A094120 A066423 * A072498 A162643 A072587
KEYWORD
nonn
AUTHOR
Luca Onnis, Jul 07 2022
STATUS
approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 21 09:23 EDT 2024. Contains 373542 sequences. (Running on oeis4.)