A326183 -id:A326183 - cp's OEIS frontend

A326182 Numbers for which A003961(n) <= A064989(sigma(A003961(n))).

1, 4, 9, 36, 64, 169, 256, 576, 625, 676, 729, 1024, 1369, 1521, 1600, 2304, 2500, 2809, 2916, 3136, 4096, 4489, 5184, 5476, 5625, 6084, 6561, 6889, 7396, 7744, 9216, 9409, 10816, 11236, 12321, 14400, 14641, 16129, 17956, 19044, 22500, 23104, 24964, 25281, 26244, 26569, 27556, 27889, 28224, 28561, 33856, 36864, 37636, 40000, 40401

Offset: 1

Antti Karttunen, Jun 16 2019

nonn

Not all terms are squares: the first nonsquare occurs as a(1427) = 97560000 = 2^6 * 3^2 * 5^4 * 271, and among the first 4011 terms (those <= 2^30), there are 24 of them, see A326183.

Cf. A000203, A000290, A003961, A064989, A286385, A326042, A326183 (nonsquares present).

A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
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)};
isA326182(n) = { my(u=A003961(n)); (u <= A064989(sigma(u))); };

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

A326182 Numbers for which A003961(n) <= A064989(sigma(A003961(n))).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI