A361469 a(n) = bigomega(A249670(A003961(n))).

0, 3, 3, 3, 4, 4, 4, 7, 3, 7, 3, 4, 4, 5, 7, 6, 4, 6, 5, 7, 7, 6, 4, 6, 4, 5, 7, 5, 6, 8, 3, 9, 6, 7, 8, 6, 4, 6, 7, 11, 4, 8, 6, 4, 7, 5, 5, 7, 4, 5, 5, 3, 5, 8, 5, 9, 8, 9, 3, 8, 4, 6, 7, 7, 8, 7, 6, 7, 5, 9, 3, 8, 6, 5, 7, 6, 7, 8, 5, 10, 6, 7, 5, 6, 8, 7, 9, 10, 4, 10, 8, 5, 6, 6, 9, 10, 4, 7, 6, 5, 5, 6, 6, 7, 11

Offset: 1

Author

Antti Karttunen, Mar 20 2023

Keywords

• nonn

Comments

Conjecture: There are no 1's in this sequence. If true, it would imply that there are no odd terms in A065997.

The first n with a(n) = 2 is 1684804. Note that A003961(1684804) = 5659641 is so far the only known odd term in A247086.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A001222, A003961, A065997, A247086, A249670, A361468.

Programs

PARI

A003961(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From A003961
A249670(n) = { my(ab = sigma(n)/n); numerator(ab)*denominator(ab); };
A361469(n) = bigomega(A249670(A003961(n)));

Formula

a(n) = A001222(A361468(n)) = A001222(A249670(A003961(n))).