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

Author

Antti Karttunen, Jun 16 2019

Keywords

• nonn

Comments

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.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..4011; all terms up to 2^30
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

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

Programs

PARI

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))); };