A336849 a(n) = A003961(n) / gcd(A003961(n), sigma(A003961(n))), where A003961 is the prime shift towards larger primes.

1, 3, 5, 9, 7, 5, 11, 27, 25, 21, 13, 15, 17, 11, 35, 81, 19, 75, 23, 63, 55, 39, 29, 9, 49, 17, 125, 33, 31, 35, 37, 243, 65, 57, 77, 225, 41, 23, 85, 189, 43, 55, 47, 9, 175, 29, 53, 135, 121, 49, 19, 17, 59, 125, 13, 99, 115, 93, 61, 105, 67, 111, 275, 729, 119, 65, 71, 171, 29, 77, 73, 135, 79, 41, 245, 69, 143

Offset

1,2

Comments

If there are no more 1's in this sequence after the initial one, then there are no odd terms of A007691 (multiply perfect numbers) larger than one.

Denominator of the ratio A003973(n) / A003961(n), also denominator of the ratio (A341528(n)/A341529(n)) / (n / sigma(n)). - Antti Karttunen, Feb 16 2021

Links

Antti Karttunen, Table of n, a(n) for n = 1..16383

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

Formula

a(n) = A003961(n) / A336850(n) = A003961(n) / gcd(A003961(n), A003973(n)).

a(n) = A017666(A003961(n)).

Mathematica

f[p_, e_] := NextPrime[p]^e; g[1] = 1; g[n_] := Times @@ f @@@ FactorInteger[n]; a[n_] := (gn = g[n])/GCD[gn, DivisorSigma[1, gn]]; Array[a, 100] (* Amiram Eldar, Feb 17 2021 *)

Prog

(PARI)
A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A336849(n) = { my(u=A003961(n)); (u/gcd(u, sigma(u))); };
\\ Or alternatively as:
A336849(n) = { my(u=A003961(n)); denominator(sigma(u)/u); };

Crossrefs

Cf. A003961, A003973, A007691, A017666, A336848, A336850, A341528, A341529, A341530.

Cf. A341525 (numerators).

Sequence in context: A340593 A021282 A016613 * A348994 A079427 A168271

Adjacent sequences: A336846 A336847 A336848 * A336850 A336851 A336852

Keyword

nonn,frac

Author

Antti Karttunen, Aug 06 2020

Status

approved