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A342665
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Numbers k for which phi(k)+1 is a multiple of d(k), where phi is Euler totient function (A000010) and d(n) gives the number of divisors of n (A000005).
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2
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1, 2, 4, 25, 81, 121, 289, 529, 841, 1681, 2209, 2809, 3481, 5041, 6889, 7921, 10201, 11449, 12100, 12769, 17161, 18769, 22201, 27889, 28561, 28900, 29929, 32041, 36481, 38809, 51529, 54289, 57121, 63001, 66049, 69169, 72361, 78961, 84100, 85849, 96721, 100489, 120409, 124609, 128881, 146689, 151321, 160801, 175561
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OFFSET
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1,2
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COMMENTS
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Numbers k such that A124331(k) = k. This is also a subsequence of the records of A124331 (both their values and their positions).
Terms other than 2 are a perfect square. Proof: phi(k) is even for k > 2. So phi(k)+1 is odd for k > 2. d(k) is odd only if k is a perfect square. So for any term k > 2 we need k to be a perfect square. Checking cases <= 2 leaves only 2 as the nonsquare in this sequence. - David A. Corneth, Mar 31 2021
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LINKS
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MATHEMATICA
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Select[Join[{1, 2}, Range[2, 420]^2], Divisible[EulerPhi[#] + 1, DivisorSigma[0, #]] &] (* Amiram Eldar, Mar 31 2021 *)
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PROG
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(PARI) isA342665(n) = !((eulerphi(n)+1) % numdiv(n));
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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