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

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

Author

Antti Karttunen, Aug 26 2020

Keywords

• nonn

Comments

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.

Links

• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Odd terms of A337343.

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

Programs

PARI

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));