A337340 a(n) = (A337339(n)-A003961(n)) / 2.

0, 1, 4, 16, 9, 49, 25, 169, 144, 100, 36, 484, 64, 38, 289, 1600, 81, 1369, 121, 961, 729, 361, 196, 4489, 576, 625, 3844, 139, 225, 2704, 324, 14641, 1024, 784, 1444, 12544, 400, 1156, 1764, 8836, 441, 6724, 529, 3364, 7569, 1849, 676, 40804, 3600, 5329, 2209, 5776, 841, 34969, 2025, 4262, 3249, 386, 900, 24649, 1089

Offset

1,3

Comments

Not all terms are squares. For example, a(14) = 38, a(28) = 139 and a(56) = 4262 are not squares.

Not all terms are nonnegative. The first three negative terms are a(1354) = -290, a(7078) = -1363 and a(15722) = -2386.

Links

Antti Karttunen, Table of n, a(n) for n = 1..8191

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

Prog

(PARI)
A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A337340(n) = { my(h=A003961(n), s=(h^2), u=(s+1)/2); ((u/gcd(1+sigma(s), u)) - h)/2; };

Crossrefs

Cf. A003961, A337337, A337339.

Cf. also A337341.

Sequence in context: A228561 A049208 A316274 * A061093 A067178 A346460

Adjacent sequences: A337337 A337338 A337339 * A337341 A337342 A337343

Keyword

sign

Author

Antti Karttunen, Aug 24 2020

Status

approved