A353750 a(n) = phi(sigma(n)) * A064989(sigma(n)), where A064989 shifts the prime factorization one step towards lower primes.

1, 4, 2, 30, 4, 8, 4, 48, 132, 24, 8, 60, 30, 16, 16, 870, 24, 528, 24, 120, 16, 48, 16, 96, 870, 120, 48, 120, 48, 96, 16, 720, 32, 144, 32, 3960, 306, 96, 120, 288, 120, 64, 140, 240, 528, 96, 32, 1740, 1224, 3480, 96, 1050, 144, 192, 96, 192, 96, 288, 96, 480, 870, 64, 528, 14238, 240, 192, 416, 720, 64, 192, 96

Offset

1,2

Comments

In contrast to A353749, this is not multiplicative, except on positions given by A336547.

It seems that a(n) = A353749(n) only on n=1. This would then imply that the intersection of A006872 and A336702 = {1}.

Links

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

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

Formula

a(n) = A353749(A000203(n)) = A062401(n) * A350073(n).

a(n) = A353749(n) + A353757(n).

Prog

(PARI)
A064989(n) = { my(f=factor(n>>valuation(n, 2))); for(i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f); };
A353750(n) = { my(s=sigma(n)); (eulerphi(s)*A064989(s)); };

Crossrefs

Cf. A000010, A000203, A006872, A062401, A064989, A336547, A336548, A336549, A336702, A350073, A353747, A353748, A353749.

Cf. A353757, A353758 (where a(n) < A353749(n)), A353759 (where a(n) >= A353749(n)), A353760, A353790 [= a(A003961(n))].

Cf. also A353792.

Sequence in context: A121667 A368767 A291844 * A093991 A030447 A302369

Adjacent sequences: A353747 A353748 A353749 * A353751 A353752 A353753

Keyword

nonn

Author

Antti Karttunen, May 07 2022

Extensions

Dubious comment deleted by Antti Karttunen, Jan 26 2023

Status

approved