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A337337 a(n) = gcd(1+sigma(s), (s+1)/2), where s is the square of n once prime-shifted (s = A003961(n)^2 = A003961(n^2)). 7
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 13, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 17, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,14

COMMENTS

All terms are in A007310, because all terms of A337336 are.

LINKS

Antti Karttunen, Table of n, a(n) 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) = gcd((s+1)/2, 1+sigma(s)), where s = A003961(n)^2 = A003961(n^2).

a(n) = gcd(A048673(n^2), 1+A003973(n^2)).

a(n) = gcd(A048673(n^2), A337194(A003961(n)^2)) = gcd(A337336(n), A336844(n^2)).

a(n) = A336697(A048673(n)).

a(n) = A337335(n^2).

PROG

(PARI)

A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };

A337337(n) = { my(s=(A003961(n)^2)); gcd((s+1)/2, 1+sigma(s)); };

(PARI)

A048673(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); (factorback(f)+1)/2; };

A336697(n) = { my(s=((n+n-1)^2)); gcd((s+1)/2, 1+sigma(s)); };

A337337(n) = A336697(A048673(n));

CROSSREFS

Cf. A003961, A003973, A007310, A048673, A336697, A336844, A337194, A337335, A337336, A337338, A337339.

Sequence in context: A326073 A257098 A322356 * A119788 A334561 A059592

Adjacent sequences:  A337334 A337335 A337336 * A337338 A337339 A337340

KEYWORD

nonn

AUTHOR

Antti Karttunen, Aug 24 2020

STATUS

approved

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Last modified July 30 18:40 EDT 2021. Contains 346359 sequences. (Running on oeis4.)