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 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 Table of n, a(n) for n=1..65. 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). Cf. A007956, A052485, A106543. Sequence in context: A010386 A094120 A066423 * A072498 A162643 A072587 Adjacent sequences: A355568 A355569 A355570 * A355572 A355573 A355574 KEYWORD nonn AUTHOR Luca Onnis, Jul 07 2022 STATUS approved

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