A337343 -id:A337343 - cp's OEIS frontend

A350073 a(n) = A064989(sigma(n)), where A064989 is multiplicative with a(2^e) = 1 and a(p^e) = prevprime(p)^e for odd primes p.

1, 2, 1, 5, 2, 2, 1, 6, 11, 4, 2, 5, 5, 2, 2, 29, 4, 22, 3, 10, 1, 4, 2, 6, 29, 10, 3, 5, 6, 4, 1, 20, 2, 8, 2, 55, 17, 6, 5, 12, 10, 2, 7, 10, 22, 4, 2, 29, 34, 58, 4, 25, 8, 6, 4, 6, 3, 12, 6, 10, 29, 2, 11, 113, 10, 4, 13, 20, 2, 4, 4, 66, 31, 34, 29, 15, 2, 10, 3, 58, 49, 20, 10, 5, 8, 14, 6, 12, 12, 44, 5, 10

Offset: 1

Antti Karttunen, Dec 12 2021

Cf. A000203, A064989, A161942, A337343 (a(n) >= n), A348748, A348749.

Cf. also A326042, A350072.

f[2, e_] := 1; f[p_, e_] := NextPrime[p, -1]^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[DivisorSigma[1, n]]; Array[a, 100] (* Amiram Eldar, Dec 12 2021 *)

A064989(n) = { my(f = factor(n)); for (i=1, #f~, f[i,1] = if(2==f[i, 1],1,precprime(f[i, 1]-1))); factorback(f); };
A350073(n) = A064989(sigma(n));

Multiplicative with a(p^e) = A064989(1 + p + p^2 + ... + p^e).

a(n) = A064989(A000203(n)) = A064989(A161942(n)).

A337344 Odd numbers k such that A064989(sigma(k)) >= k.

Original entry on oeis.org

1, 9, 25, 225, 289, 729, 1681, 2401, 2601, 3481, 5041, 6561, 7225, 7921, 10201, 15129, 15625, 17161, 18225, 19881, 21609, 27889, 28561, 29929, 31329, 35721, 42025, 45369, 59049, 60025, 62001, 65025, 71289, 83521, 85849, 87025, 88209, 91809, 114921, 123201, 126025, 130321, 140625, 146689, 154449, 164025, 172225

Offset: 1

Antti Karttunen, Aug 26 2020

nonn

Applying A064989 to these terms and sorting into ascending order gives A326182.
Conversely, this sequence is obtained when the sequence b(n) = A003961(A326182(n)) is sorted into ascending order.
Not all terms are squares. For example, 12121028325 = A003961(A326183(1)) = 3^6 * 5^2 * 7^4 * 277 is also term, and this is true for all terms of A326183 similarly prime shifted. Interestingly, for n = 1..24, A003961(A326183(n)) is a term of A228058.

Odd terms of A337343.

Cf. A000203, A003961, A064989, A228058, A326042, A326182, A326183.

A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
isA337344(n) = ((n%2)&&(A064989(sigma(n))>=n));

cp's OEIS Frontend

A350073 a(n) = A064989(sigma(n)), where A064989 is multiplicative with a(2^e) = 1 and a(p^e) = prevprime(p)^e for odd primes p.

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