A342651 - OEIS

A342651

a(n) = A329697(A156552(n)).

0, 0, 1, 0, 1, 0, 2, 1, 2, 0, 2, 0, 1, 1, 2, 0, 2, 0, 3, 2, 3, 0, 3, 1, 3, 2, 3, 0, 3, 0, 3, 1, 5, 1, 3, 0, 1, 3, 3, 0, 3, 0, 4, 2, 6, 0, 4, 1, 2, 3, 4, 0, 3, 2, 4, 5, 4, 0, 4, 0, 7, 3, 4, 1, 4, 0, 5, 1, 2, 0, 3, 0, 4, 2, 4, 1, 5, 0, 4, 2, 8, 0, 3, 3, 7, 6, 4, 0, 3, 2, 6, 4, 9, 3, 4, 0, 4, 3, 2, 0, 5, 0, 5, 3

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OFFSET

2,7

LINKS

Antti Karttunen, Table of n, a(n) for n = 2..6381 (based on Hans Havermann's factorization of A156552)

Index entries for sequences computed from indices in prime factorization

FORMULA

a(n) = A329697(A156552(n)) = A329697(A322993(n)).

a(n) = A329697(A342666(n)) + A342656(n).

a(p) = 0 for all primes p.

a(A003961(n)) = a(n).

PROG

(PARI)

A156552(n) = {my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res};

A329697(n) = { my(f=factor(n)); sum(k=1, #f~, if(2==f[k, 1], 0, f[k, 2]*(1+A329697(f[k, 1]-1)))); };

A342651(n) = A329697(A156552(n));

(PARI)

\\ Version using the factorization file available at https://oeis.org/A156552/a156552.txt

v156552sigs = readvec("a156552.txt");

A329697(n) = { my(f=factor(n)); sum(k=1, #f~, if(2==f[k, 1], 0, f[k, 2]*(1+A329697(f[k, 1]-1)))); };

A342651(n) = if(isprime(n), 0, my(prsig=v156552sigs[n], ps=prsig[1], es=prsig[2]); sum(i=2-(ps[1]%2), #ps, es[i]*(1+A329697(ps[i]-1)))); \\ Antti Karttunen, Jan 29 2022

CROSSREFS

Cf. A156552, A329697, A322993, A342652, A350067.

Cf. A000040 (positions of 0's), A350069 (of 1's).

Sequence in context: A159955 A327306 A053838 * A275768 A117167 A117169

Adjacent sequences: A342648 A342649 A342650 * A342652 A342653 A342654

KEYWORD

nonn

AUTHOR

Antti Karttunen, Mar 18 2021

STATUS

approved