A322981 If n is the k-th prime power > 1, a(n) = k, otherwise a(n) = 0.

0, 1, 2, 3, 4, 0, 5, 6, 7, 0, 8, 0, 9, 0, 0, 10, 11, 0, 12, 0, 0, 0, 13, 0, 14, 0, 15, 0, 16, 0, 17, 18, 0, 0, 0, 0, 19, 0, 0, 0, 20, 0, 21, 0, 0, 0, 22, 0, 23, 0, 0, 0, 24, 0, 0, 0, 0, 0, 25, 0, 26, 0, 0, 27, 0, 0, 28, 0, 0, 0, 29, 0, 30, 0, 0, 0, 0, 0, 31, 0, 32, 0, 33, 0, 0, 0, 0, 0, 34, 0, 0, 0, 0, 0, 0, 0, 35

Offset: 1

Author

Antti Karttunen, Jan 01 2019

Keywords

• nonn

Comments

This is a ("corrected") variant of A095874, which uses the list of "powers of primes" A000961 instead of prime powers A246655. - M. F. Hasler, Jun 16 2021

Links

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

Crossrefs

Cf. A000961 (powers of primes, including 1), A010055, A025528, A069513, A095874 (analog based on A000961), A246655 (prime powers > 1).

Cf. A049084.

Programs

PARI

up_to = 16384;
A322981list(up_to) = { my(v=vector(up_to), k=0); for(n=1,up_to,if(isprimepower(n),k++; v[n] = k, v[n] = 0)); (v); };
v322981 = A322981list(up_to);
A322981(n) = v322981[n];

PARI

A322981(n)=if(isprimepower(n),sum(i=1,exponent(n),primepi(sqrtnint(n,i)))) \\ M. F. Hasler, Jun 16 2021

Formula

a(n) = A010055(n) * A025528(n) = A069513(n) * A025528(n).

a(n) = A025528(A069513(n)*n), when assuming that A025528(0) = 0.

a(A000961(1+n)) = n for all n >= 1.