A344537 Inverse permutation to A344535.

0, 1, 2, 4, 8, 3, 64, 5, 16, 9, 1024, 6, 32768, 65, 10, 32, 2097152, 17, 268435456, 12, 66, 1025, 68719476736, 7, 128, 32769, 18, 68, 35184372088832, 11, 36028797018963968, 33, 1026, 2097153, 72, 20, 73786976294838206464, 268435457, 32770, 13

Offset: 1

Author

Rémy Sigrist, May 23 2021

Keywords

• nonn
• base

Comments

This sequence is additive.

This sequence establishes a bijection from A225547 to A261195.

Examples

			A344535(42) = 240, so a(240) = 42.
		

Links

• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A000120, A006125, A036442, A064547, A225546, A225547, A261195, A344535, A344536.

Programs

PARI

a(n) = { my (f=factor(n), v=0); for (k=1, #f~, my (x=primepi(f[k, 1])-1, yy=f[k, 2], y); while (yy, yy-=2^y=valuation(yy, 2); v+=2^(y + (x+y)*(x+y+1)/2))); v }

Formula

a(prime(n)) = A006125(n+1) for any n >= 0.

a(2^2^n) = A036442(n).

A000120(a(n)) = A064547(n).

a(A225546(n)) = A344536(n).

a(n) = A344536(n) iff n belongs to A225547.