A324891 a(n) = sigma(A170818(n)), where A170818(n) is the part of n composed of prime factors of form 4k+1.

1, 1, 1, 1, 6, 1, 1, 1, 1, 6, 1, 1, 14, 1, 6, 1, 18, 1, 1, 6, 1, 1, 1, 1, 31, 14, 1, 1, 30, 6, 1, 1, 1, 18, 6, 1, 38, 1, 14, 6, 42, 1, 1, 1, 6, 1, 1, 1, 1, 31, 18, 14, 54, 1, 6, 1, 1, 30, 1, 6, 62, 1, 1, 1, 84, 1, 1, 18, 1, 6, 1, 1, 74, 38, 31, 1, 1, 14, 1, 6, 1, 42, 1, 1, 108, 1, 30, 1, 90, 6, 14, 1, 1, 1, 6, 1, 98, 1, 1, 31, 102, 18, 1, 14, 6

Offset

1,5

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Index entries for sequences related to sigma(n)

Formula

Multiplicative with a(p^e) = (p^(e+1) - 1)/(p-1) if p == 1 (mod 4), otherwise a(p^e) = 1.

a(n) = A000203(A170818(n)).

a(n) = A000593(n) / A324893(n).

Prog

(PARI) A324891(n) = { my(f=factor(n)); prod(i=1, #f~, if(f[i, 1]%4>1, 1, ((f[i, 1]^(1+f[i, 2]))-1)/(f[i, 1]-1))); };
(PARI)
A170818(n) = { my(f=factor(n)); prod(i=1, #f~, if(f[i, 1]%4>1, 1, f[i, 1])^f[i, 2]); }; \\ From A170818
A324891(n) = sigma(A170818(n));

Crossrefs

Cf. A000203, A000593, A170818, A324893.

Sequence in context: A080219 A339747 A293901 * A260340 A040037 A344877

Adjacent sequences: A324888 A324889 A324890 * A324892 A324893 A324894

Keyword

nonn,mult

Author

Antti Karttunen, Mar 27 2019

Status

approved