A289623 a(n) = A055396(A048673(n)).

0, 1, 2, 3, 1, 1, 1, 1, 6, 5, 4, 9, 2, 7, 1, 13, 1, 1, 1, 1, 1, 1, 2, 1, 3, 1, 2, 1, 1, 16, 8, 1, 2, 10, 2, 30, 2, 3, 14, 3, 1, 23, 1, 17, 1, 1, 2, 4, 18, 1, 1, 4, 1, 1, 1, 35, 1, 15, 11, 1, 1, 1, 1, 3, 1, 1, 1, 1, 21, 1, 12, 1, 1, 1, 2, 1, 1, 1, 1, 1, 65, 3, 2, 1, 19, 20, 1, 1, 4, 56, 1, 32, 2, 1, 2, 1, 2, 1, 38, 6

Offset: 1

Author

Antti Karttunen, Jul 16 2017

Keywords

• nonn
• look

Comments

From the scatter plot it can be seen that the terms are grouped into two distinct populations by their magnitude, with significant gap between them.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A048673, A055396, A246263 (the positions of ones).

Cf. also A278224, A286582, A286583, A286584, A286586.

Programs

PARI

A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ This function from Michel Marcus
A048673(n) = (A003961(n)+1)/2;
A055396(n) = if(n==1, 0, primepi(factor(n)[1, 1])); \\ This function from Charles R Greathouse IV, Apr 23 2015
A289623(n) = A055396(A048673(n));

Formula

a(n) = A055396(A048673(n)).